Summer Math Packet Help?

Question

The retards at our school decided to give us math packets based on the grade we are going INTO. I honestly cant figure out half this stuff. Please help.

1) What is the minimum value given the following constraints?

Objective quantity: C = 37x + 52y

Constraints:

x {less than/equal to} 0

y {greater than/equal to} 0

6x - 5y = -300

3x + 8y = -24

A) 3120

B) -856

C) -296

D) No minimum

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2) What is the minimum value given the following constraints?

Objective quantity: C = 3x - 5y

Constraints:

x {greater than/equal to} 0

y {greater than/equal to} 0

3x - 2y = 12

5x + 2y = 20

A) -50

B) 12

C) -30

D) No minimum

Answer 1

1) Solve for x and y as follows:

6x-5y=-300 now multiply bottom equation by -2 to get -6x -16y=48.  Cancel the x's, get -21y=-252, y=12.  Now use 3x+8y=-24 with y=12, solve for x, get 3x=-120, x=-40.  This satisfies the contraints that y must be at least 0 and x must be at most 0.  Now plug in x and y into C=37x + 52y get C=37(-40) + 52(12) get C=-1480+624 so C=-856 which is B.

2) Same strategy here, good luck.