Mark M. answered • 07/03/20

Test Prep Expert Wants to Make You a Better Person

Let: P= Total profit, S= Total sets

A= number of sets of Model A

B= number of sets of Model B

** Goal:** Maximize: P(A,B) = 60A + 40B

__Constraints__:

A + B <= 60

30 <= A <= 60

20 <= B <= 30

While plotting A vs. B on a graph is acceptable, I would generate vertices (A,B) directly from the constraints.

__Using the theory that the optimal solution in goal programming lies along an edge between 2 vertices (and typically at the vertices), we can deduce__:

A=30 --> B=30 (30,30)

note: Any A>30 does not yield an acceptable value of B

B=20 --> A=40 (40,20)

B=30 --> A=30 (same as above)

**So the solution lies along the edge (40,20), (30,30)**

Plug these values into the profit function (which is to be maximized) P= 60A + 40B

(40,20) --> P = 60(40) + 40(20) = 3200

(30,30) --> P = 60(30) + 40(30) = 3000

**Therefore profit is optimized when A = 40 sets and B = 20 sets**