What is the maximum value of P = 2x + 5y subject to the constraints x

Question

What is the maximum value of  P = 2x + 5y  subject to the constraints  x \leq y ,  3x - y \geq 1 , and  3x + y \leq 5  ?

(A) 3.5
(B) 8.75
(C) 12
(D) 12.25
(E) 14

Tulkin987 · Answer

3x - y \geq 1  -->  y \leq 3x-1 
 3x + y \leq 5  -->  y \leq 5-3x

From above inequalities we know that  3x-1=5-3x  -->  x=1  and  y \leq 5-3*1=2

For  x=1  and  y=2  maximum value of  P = 2x + 5y = 2+10 = 12

Answer: C

RohitGoyal1123 · Answer

The favorable region formed by the inequalities is a triangle with vertexes as A  (\frac{1}{2},\frac{1}{2}) ; B  (\frac{5}{4}, \frac{5}{4})  and C (1,2)

Now for P to be max, we can replace x,y as point C

Hence P = 2*1 + 2*5 = 12

Hence  C

huytm1912 · Answer

Answer is E,
we solved that at above Y<= 2, so 5y<=10. x<=y, so 2x<=2y it means that 2x<=10. Therefore, 2x+5y <= 10+4 = 14

LevanKhukhunashvili · Answer

huytm1912

y=2 and x=2 does not satisfy the stem 3x+y≤5

HisHo · Answer

Hi  Tulkin987 
Why you converted the inequality to equality in the last 2 lines?
I mean we still need to say that y≤2 and x≥1

Tulkin987 · Answer

3x - y \geq 1  -->  y \leq 3x-1  and
 3x + y \leq 5  -->  y \leq 5-3x  
together imply that  3x-1=5-3x  and  y \leq 2

Thus,  x=1  and  y=2 .

Hope this helps.

KSBGC · Answer

Condition:

x \leq y

we see inequalities are given in opposite direction thus we can deduct negative one from positive one.

3x - y -3x - y \leq 1 - 5

-2y \leq -4

y \geq 2

y ( mx) = 2

what about x?

we are looking for max value of the given equation thus we will try to maximize both x and y.

y=2

but x must not be 2 although it is given that  x \leq y .

3x + y \leq 5

This condition compels us to keep the value of x = 1.

P = 2x + 5y

P = 2*1 + 5*2 = 12.

C is the correct answer.

siddharth_ · Answer

3x-y>=1 and -3x-y>=-5 ——> -2y >=-4 or y<=2
For P = 2x + 5y to be max, y = 2

Putting y in 1st; 3x - 2 >=1 or x >= 1
Putting y in 2nd; 3x + 2 <= 5 or x <= 1
From the 2 constraints above, x = 1

Thus, P(max) = 2+10 =12

Kinshook · Answer

What is the maximum value of  P = 2x + 5y  subject to the constraints  x \leq y ,  3x - y \geq 1 , and  3x + y \leq 5  ?

P = 2x + 5y

x \leq y 
 3x - y \geq 1  - >  y \leq 3x-1 
 3x + y \leq 5  - >   y \leq 5-3x

There are 3 intersection points A(.5,.5), B (1,2) & C (1.25,1.25)

At A(.5,.5) : P = 2x + 5y = 3.5
At B (1,2) : P = 2x + 5y = 12
At C (1.25,1.25): P = 2x + 5y = 8.75

P is max at B(1,2) = 12

IMO C

ZIX · Answer

Why can't I add ---->  x≤y  and  3x+y≤5  ----> to form  4x + y ≤ 5 + y  ---->  x ≤ \frac{5}{4}

What is the maximum value of P = 2x + 5y subject to the constraints x

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GMAT Problem Solving (PS) Questions

What is the maximum value of P = 2x + 5y subject to the constraints x

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards