Question

Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)

Answer 1

Answer:

Maximize C =$9x + 7y$

$8x + 10y \leq 17$

$11x + 12y\leq 25$

and x ≥ 0, y ≥ 0

Plot the lines on graph

$8x + 10y \leq 17$

$11x + 12y\leq 25$

$x\geq 0$

$y\geq 0$

So, boundary points of feasible region are (0,1.7) , (2.125,0) and (0,0)

Substitute the points in  Maximize C

At  (0,1.7)

Maximize C =$9(0) + 7(1.7)$

Maximize C =$11.9$

At  (2.125,0)

Maximize C =$9(2.125) + 7(0)$

Maximize C =$19.125$

At   (0,0)

Maximize C =$9(0) + 7(0)$

Maximize C =$0$

So, Maximum value is attained at   (2.125,0)

So, the optimal value of x is 2.125

The optimal value of y is 0

The maximum value of the objective function is 19.125