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555-605 Level|   Graphs|   Math Related|      
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catinabox
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A food manufacturer has created four prototypes of a new product to be 24 Aug 2024, 15:30
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Dropdown 1: Prototype C Dropdown 2: 17
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25% (medium)

Question Stats:

87% (02:16) correct 13% (02:49) wrong based on 318 sessions

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A food manufacturer has created four prototypes of a new product to be launched next year. Each prototype contains three main ingredients—fruit, wheat flour, and chocolate—in varying proportions, as shown in the first graph. The cost per pound (Price/lb) for each ingredient is shown in the second graph.

From each drop-down menu, select the option that creates the most accurate statement according to the information provided.

Assuming that all prototypes weigh the same, the product with the lowest total cost per unit is , with a per-pound product cost of .
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Dropdown 1: Prototype C Dropdown 2: 17
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A food manufacturer has created four prototypes of a new product to be 05 Sep 2024, 10:28
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catinabox

A food manufacturer has created four prototypes of a new product to be launched next year. Each prototype contains three main ingredients—fruit, wheat flour, and chocolate—in varying proportions, as shown in the first graph. The cost per pound (Price/lb) for each ingredient is shown in the second graph.

From each drop-down menu, select the option that creates the most accurate statement according to the information provided.

Assuming that all prototypes weigh the same, the product with the lowest total cost per unit is , with a per-pound product cost of .
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Official Solution:

Looking at the second chart, we see that Wheat is the cheapest ingredient, while Chocolate is the most expensive. Since all products weigh the same, it’s reasonable to assume that the cheapest product will be the one that uses the highest percentage of Wheat and the lowest percentage of Chocolate. This is our initial assumption going into the question.

From the first graph, we can identify that Prototype C fits this pattern—it contains 50% Wheat and only 10% Chocolate, making it the likely cheapest product. There’s no need to calculate the exact cost to determine the answer or compare the other prototypes.

For the second dropdown, however, we do need the exact cost of the cheapest product.

Calculating the cost for Prototype C, we get: 0.4 * 20 + 0.5 * 10 + 0.1 * 40 = 17.


Correct answer:

Dropdown 1: "Prototype C"

Dropdown 2: "17"
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A food manufacturer has created four prototypes of a new product to be 25 Aug 2024, 04:30
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1) look for largest proportion of Wheat Flour along with least proportion of Chocolate => Prototype C

2) 0.4*20+0.5*10+0.1*40=17­
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A food manufacturer has created four prototypes of a new product to be 03 Sep 2024, 08:16
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1) look for largest proportion of Wheat Flour along with least proportion of Chocolate => Prototype C

2) 0.4*20+0.5*10+0.1*40=17­
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­This is the correct and the easiest way to figure out this question!

The trick to not doing needless calculations was to identify that Prototype C has the largest proportion of the cheapest ingredient (wheat flour), along with the smallest proportion of the most expensive ingredient (chocolate).­

However, note that this works only when there is a significant price delta between the ingredients. You'd want to be careful with shortcuts when the ingredients are similarly priced.
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A food manufacturer has created four prototypes of a new product to be 24 Oct 2024, 21:25
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for drop down 1:
wheat has to be in larger portion followed by rice and chocolate, so option C.
for drop down 2:
(50*10)+(40*20)+(10*40)/100
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