Maximize (math w applications)?

Question

The question goes as fallowing;

Model A 15min(Ea) Assemble 10(ea) Packing
Model B 10min (ea) assemble 12(ea) Packing
-------------------------------------------------------------------------'
Totals 1500 min 1320min

Profit Model A = 12$
Profit Model B = 10$

How many of each model should be produced for max profit?

What is the maximum profit?

(You may solve graphically or by simplex)

Thank you

Answer 1

Constraints:
15A+10B ≤ 1500
10A + 12B ≤ 1320

Objective:
Profit = f(A, B) = 12A + 10B
maximum profit = f(60,60) = $1320
----------
Ideas: The maximum value must occur at one of the vertexes. But in reality, you can tell which vertex gives you the maximum by comparing slopes or just looking at the region directly.

Answer 2

A is number of model A's, B the number of B's, produced.
Constraints:
15A + 10B ≤ 1500
10A + 12B ≤ 1320

graph of 1st has A intercept at 100, B at 150. graph of 2nd has A at 132, B at 110. solve system for intersection:
30A + 36B = 3960
30A + 20B = 3000
16B = 960
B = 60
15A + 10(60) = 1500
15A = 900
A = 60

we could test the value of the profit function at (132,0), all A, (0,150), all B, and (60,60), the mix, but since the slope of the profit function is BETWEEN the slopes of the constraints, we know to pick (60,60), and get 12(60) + 10(60) = 720 + 600 = $1320.

Glad this was high school easy. Way too long since I visited the simplex method.