Linear programming algebra question

Question

a manufacturer of golf clubs makes a profit of $50 per set on a model A set and $45 per set on a model B set. Daily production of the model A clubs is between 30 and 50 sets, inclusive, and that of the Model B clubs is between 10 and 20 sets, inclusive. The total daily production is not to exceed 50 sets. How many sets of each model should be manufactured per day to maximize the profit. 

Answer 1

Profit ( A, B) = 50A + 45B

 

The constraints are:

30 <= A <= 50

10 <= B < 20

 

A+B <= 50

 

 

The feasibility region is a triangle with vertices (30,20)  ,  (40,10),   and  (30,10)

 

 

THe profits at these vertices are 50*30 + 20*45 = 1500 + 900 = 2400

                                              50*40 + 20*10 = 2000 + 200 = 2200

                                              50*30 + 20*10 = 1500 + 200 = 1700

 

Max profit at A=30 , B=20