Minimize C=3x+y given the constraints.

Question

Minimize C=3x+ygiven the constraints.

{0≤x≤8

{0≤y≤6

{−8x+4y≤16

{2x+y≥4

 

If the answer is not an integer, enter it as a fraction.

Answer 1

Minimize means to have the lowest value of C possible.

 

First lets find x and y from the system of equation condition.

 

Substitute 2x + y ≥ 4  into -8x + 4y ≤ 16

 

since we have equal to in the inequality, we can use the equal sign.

 

-8x + 4(4 - 2x) = 16

-8x + 16 - 8x = 16

-16x + 16 = 16

-16x = 0

    x = 0

 

Substitute this value of x into the last condition.

 

2(0) + y = 4

          y = 4

        

 

These x and y values satisfy the first two conditions.  Lets use these value to evaluate C.

 

C = 3(0) + 4

C = 4