Question

Find the optimal solution for the following problem

Answer 1

Answer:

Minimize C =$13x + 3y$

$12x + 14y \geq 21$

$15x + 20y \geq 37$

and x ≥ 0, y ≥ 0.

Plot the the lines on the graph and find the feasible region

$12x + 14y \geq 21$  -- Blue

$15x + 20y \geq 37$ --- Green

So, the boundary points of feasible region are (-3.267,4.3) , (0,1.85) and (2.467,0)

Substitute the value in Minimize C

Minimize C =$13x + 3y$

At (-3.267,4.3)

Minimize C =$13(-3.267) + 3(4.3)$

Minimize C =$-29.571$

At (0,1.85)

Minimize C =$13(0) + 3(1.85)$

Minimize C =$5.55$

At (2.467,0)

Minimize C =$13(2.467) + 3(0)$

Minimize C =$32.071$

So, the optimal value of x is -3.267

So, the optimal value of y is 4.3

So, the minimum value of the objective function is -29.571