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Given capacity: N(120) P(90) K(60)
N: P : K
G -> 3 : 2 : 1 -> to maximize: limiting factor N -> 3*40 = 120 + 2*40 = 80 + 1*40 = 40 => 240
R -> 2 : 1 : 2 -> to maximize: limiting factor K -> 2*30 = 60 + 1*30 = 30 + 2*30 = 60 => 150
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green has an N : P : K ratio by weight of 3 : 2 : 1.
Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2.

The gardener will make only one blend, either Blend Green or Blend Rich, using only the nutrients in the inventory.

Select for Blend Green the maximum amount, in grams, of Blend Green that the gardener can prepare, and select for Blend Rich the maximum amount, in grams, of Blend Rich that the gardener can prepare, according to the information provided. Make only two selections, one in each column.
The farmer can prepare dry fertiliser by using three granular nutrients: Nitrogen (N), Phosphorus (P) and Potassium (K).

The current inventory at hand is: Nitrogen 120 grams, Phosphorus 90 grams, and Potassium 60 grams.

There are two blends available : Blend green and blend rich.

We need to find the maximum quantity of Blend Green mixture that can be made.

Blend Green : (N: P: K) = 3:2:1 = 3x : 2x : x

If we take x =60, 2x =120 > permissible limit of Phosphorus 90 grams.

Let’s take x = 40,

3x = 3*40 = 120 grams.

2x = 2*40 = 80 grams.

x = 40 grams

Total weight of Blend Green = 120 + 80 + 40 = 240 grams.

The ratio of Blend Rich (N: P: K) = 2 : 1 : 2 = 2y : y : 2y

To maximise , we need to increase N.

2y =120 , then y =60 , but potassium is only 60. The ratio of potassium is 2y = 2*60 =120 > allowed limit.

so, y = 30

N = 2y = 2*30 =60

P = y = 30

K = 2*y = 2*30 = 60

Total weight = 60 + 30 + 60 = 150 grams.

Maximum weight of Blend Rich = 150 grams.


Blend Green = 240

Blend Rich = 150
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Inventory: N: 120g, P: 90g, K: 60g
Blend Green: 3:2:1 (k = 120/3=40part): 120g N: 80g P : 40g K. Total sum = 240g maximum
Blend Rich: 2:1:2 (k=60/2=30part): 60g N : 30g P : 60 g K. Total sum = 150g maximum
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green has an N : P : K ratio by weight of 3 : 2 : 1.
Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2.

The gardener will make only one blend, either Blend Green or Blend Rich, using only the nutrients in the inventory.

Select for Blend Green the maximum amount, in grams, of Blend Green that the gardener can prepare, and select for Blend Rich the maximum amount, in grams, of Blend Rich that the gardener can prepare, according to the information provided. Make only two selections, one in each column.


NPK
Avail1209060
Green3x2xx
Rich2yy2y

Trick is to find which chemical acts as a limiting factor for composition and start with that
Blend Green:
To maximize amount 3x =120
x = 40
N = 120, P = 80, K = 40, Sum = 240

Blend Rich
To maximize amount 2y=60, y = 30
N = 60, P=30, K = 60, Sum = 150

Green = 240
Rich = 150
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N=120
P=90
K=60
Bled green= 3:2:1
Sum of Ratio: 3+2+1= 6
NN limit is 120/3 = 40
Total Blend weight = sum of ratio x true scale; 6 x 40= 240
Blend Rich: 2:2:1
Match the smallest Ratio ; P =60 and ratio part 2
Total scale will be 60/2= 30
Total blend weight= 2+1+2 x 30 = 150

Final Answer: Green= 240g
Rich = 150 g
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green has an N : P : K ratio by weight of 3 : 2 : 1.
Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2.

The gardener will make only one blend, either Blend Green or Blend Rich, using only the nutrients in the inventory.

Select for Blend Green the maximum amount, in grams, of Blend Green that the gardener can prepare, and select for Blend Rich the maximum amount, in grams, of Blend Rich that the gardener can prepare, according to the information provided. Make only two selections, one in each column.
N = 120 gram
P = 90 gram
k = 60 gram

Blend green ratio = 3:2:1

Blend rich = 2:1:2

here we need to find bottleneck for each blend, and try to get maximum amount out of it

for blend green we see that we have 1 K and we can't have more than 40 gram of it because we have max 120 gram of N

So total blend green will be 40 * 3 + 40 * 2 + 40 * 1 = 240 gram


Now for blend rich, maximum K can be 30 (as it is the limit 2 * 30 = 60) so that's our bottleneck

Total = 30 * 2 + 30 * 1 + 30 * 2 = 150

Our answer is 240 and 150
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Blend Green
N = 3/6 = 1/2 of the weight.
P = 2/6 = 1/3 of the weight.
K = 1/6 of the weight.

Let's test options, we will start with the largest values.
1/2 of 300 is 150, not enough N.
1/2 of 270 is 135, not enough N.
1/2 of 240 is 120, sufficient N. 1/3 of 240 is 80, sufficient P. 1/6 of 240 is 40, sufficient K. So a maximum of 240 grams of Blend Green can be made.
------------------
Blend Rich
N = 2/5
P = 1/5
K = 2/5

2/5 of 300 is 120, sufficient N. But not for K.
2/5 of 270 is 108, sufficient N, not for K
2/5 of 240 is 96, sufficient N, not K.
2/5 of 180 is 72, not enough K.
2/5 of 150 is 60, sufficient N, and K. 1/5 of 150 is 30, sufficient P. So a maximum of 150 grams of Blend Rich can be made.
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green has an N : P : K ratio by weight of 3 : 2 : 1.
Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2.

The gardener will make only one blend, either Blend Green or Blend Rich, using only the nutrients in the inventory.

Select for Blend Green the maximum amount, in grams, of Blend Green that the gardener can prepare, and select for Blend Rich the maximum amount, in grams, of Blend Rich that the gardener can prepare, according to the information provided. Make only two selections, one in each column.
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green has an N : P : K ratio by weight of 3 : 2 : 1.
Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2.

The gardener will make only one blend, either Blend Green or Blend Rich, using only the nutrients in the inventory.

Select for Blend Green the maximum amount, in grams, of Blend Green that the gardener can prepare, and select for Blend Rich the maximum amount, in grams, of Blend Rich that the gardener can prepare, according to the information provided. Make only two selections, one in each column.


finidnig limimting factor in blend green
if we use all 120 gm on N,
we need 80gm of P
we need 40gm of K
this is also limimting factor so answer is max
240gm


in blend rich limitming factor is K
so for K = 60gm
we need P - 30gm
we need N = 60
total 150gm
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Let Blend green mixture content be in the ratio 3x:2x: x for N : P : K , and 2y: y: 2y for Blend rich. Blend green total mixture content will be 6x and Blend rich total mixture content will be 5y. In order to find maximum mixture content for Blend green we need to check inventory. Inventory contains N : 120 gms , P : 90 gms , K : 60 gms. So , Let's take 3x = 120. x = 40 , P will be 80 , K will be 40 . Also this satisfies one of the options where total value will be 6*40 = 240 gms. 270 and 300 will not be possible because it will exceed N's inventory.

So Blend green max content is 240 gms.

Similarly for Blend rich , let 2y = 60 , y=30. total value will be 5y = 5*30 = 150 gms. If we take more than this from the options , let's say 180 then y=180/5 = 36 which let to K as 72 gms exceeding inventory limit.

So Blend rich max content is 150 gms.
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green has an N : P : K ratio by weight of 3 : 2 : 1.
Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2.

The gardener will make only one blend, either Blend Green or Blend Rich, using only the nutrients in the inventory.

Select for Blend Green the maximum amount, in grams, of Blend Green that the gardener can prepare, and select for Blend Rich the maximum amount, in grams, of Blend Rich that the gardener can prepare, according to the information provided. Make only two selections, one in each column.
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Blend Green => N:P:K => 3:2:1

Clearly, if 3 units of N = 120, 2 units of p = 80 and 1 unit of k = 40 which is the max possible => total = 120+120 = 240 grams

Blend Rich =>

In this case => K will define teh units as there is not enough K to utilize with N (Ratio 1:1)

hence => 2 units k = 60, 2 units N= 60- and 1-units p = 30 => total max = 60+60+30 = 150 grams.

Blend green = 240, blend rich = 150
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N=120
P=90
K=60

Blend Green
N:P:K = 3:2:1

N: 120/3 = 40
P: 90/2 = 45
K: 60/1 = 60

Minimum value is 40 -> N is the limiting factor -> use all N
3:2:1 is 120:80:40 -> 120+80+40 = 240


Blend Rich
N:P:K = 2:1:2

N: 120/2 = 60
P: 90/1 = 90
K: 60/2 = 30

Minimum value is 30 -> K is the limiting factor -> use all K
2:1:2 is 60:30:60 -> 60+30+60 = 150

Blend Green=240
Blend Rich=150
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A gardener can prepare two types of dry fertilizer blends by mixing three granular nutrients: Nitrogen (N), Phosphorus (P), and Potassium (K). The gardener's current inventory is 120 grams of N, 90 grams of P, and 60 grams of K.

The gardener may use any amount up to the available inventory, and any unused nutrients may remain.

Blend Green: N : P : K = 3 : 2 : 1
Total parts = 3+2+1= 6
Lets take x per grams,
Nitrogen= (3/6)x = x/2
Phosphorus= (2/6)x = x/3
Potassium= (1/6)x
Inventory limits are,
(x/2)≤120 or x≤240
(x/3)≤90 or x≤270
(x/6)≤60 or x≤360
Maximum possible= 240 grams

Blend Rich: N : P : K = 2 : 1 : 2
Total parts= 2+1+2= 5
Lets take y per grams,
Nitrogen= (2/5)y
Phosphorus= (1/5)y
Potassium= (2/5)y
Inventory limits are,
(2/5)y≤120 or y≤300
(1/5)y≤90 or y≤450
(2/5)y≤60 or y≤150
Maximum possible= 150 grams

Blend Green= 240 grams
Blend Rich= 150 grams
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Blend Green
N : P : K = 3 : 2 : 1 by weight

with 120 grams of N, there are 120/3 = 40 packs at most
with 90 grams of P, there are 90/2 = 45 packs at most
with 60 grams of K, there are 60/1 = 60 packs at most

40<45<60 -> 40 packs using 120 of N, 80 of P and 40 of K = 240 grams

Blend Rich
N : P : K = 2 : 1 : 2 by weight

with 120 grams of N, there are 120/2 = 60 packs at most
with 90 grams of P, there are 90/1 = 90 packs at most
with 60 grams of K, there are 60/2 = 30 packs at most

30<60<90 -> 30 packs using 60 of N, 30 of P and 60 of K = 150 grams

Blend Green=240 and Blend Rich=150
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Blend Green has an N : P : K ratio by weight of 3 : 2 : 1

The limiting nutrient in Blend Green is N because 120/3=40 < 90/2=45 < 60

Use 120 grams of N with 80 grams of P and 40 grams of K (3:2:1 ratio) = 240 grams


Blend Rich has an N : P : K ratio by weight of 2 : 1 : 2

The limiting nutrient in Blend Rich is K because 60/2=30 < 120/2=60 < 90

Use 60 grams of N with 30 grams of P and 60 grams of K (2:1:2 ratio) = 150 grams

Blend Green=240
Blend Rich=150
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NPK
grams1209060
Blend Green321
Blend Rich212

For maximum BG, N is 120, P is 80, K is 40, Total sum is 240
For maximum BR, N is 60, P is 30,K is 60. Total sum is 150.
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120 grams of N, 90 grams of P, and 60 grams of K

Blend Green ratio by weight of 3 : 2 : 1 (N : P : K)

120 grams of N -> 120/3=40 packets
90 grams of P -> 90/2=45 packets
60 grams of K -> 60 packets

min(40,45,60) = 40 packets
In 40 packets use 120 grams of N, 80 grams of P, and 40 grams of K = 240 grams


Blend Rich ratio by weight of 2 : 1 : 2 (N : P : K)
120 grams of N -> 120/2=60 packets
90 grams of P -> 90=90 packets
60 grams of K -> 60/2=30 packets

min(60,90,30) = 30 packets
In 30 packets use 60 grams of N, 30 grams of P, and 60 grams of K = 150 grams

Blend Green=240 and Blend Rich=150
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We know that,
The gardener's current inventory holds different types of nutrients
1. Nitrogen (N)= 120g
2. Phosphorous (P) = 90g
3. Potassim (K) = 60g

Blend Green -> N:P:K = 3:2:1
Let us consider there is x grams of blend green. So,
N = 3x / 6 = x/2
P = 2x/6 = x/3
K= x/6 = x/6

Now the lowest limiting nutrient will be the possible blend green
N: x/2 <= 120 => x<= 240
P: x/3 <= 90 => x<= 270
K: x/6 <=60 => x <= 360

Therefore, we see due to nitrogen being the limiting nutrient, Blend green is 240g

Blend Rich:

N:P:K = 2:1:2

Let us consider there is y grams in Blend rich
N = 2y/5
P = y/5
K = 2y/5

Now the lowest limiting nutrient will be the possible value of blend rich
N: 2y/5 <= 120 => y <= 300
P: y/5 <= 90 => y <= 450
K: 2y/5 <= 60 => y <= 150

=> Since potassium is the limiting nutrient, blend rich is of 150g

Blend Green = 240g
Blend Rich = 150g
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