42 Ashworth Industries would like to make a price and production decision on two of its products. Define QA and QB as the quantities of products A and B to produce and PA and PB as the price for products A and B. The weekly quantities of A and B that are sold are functions of the price, according to the following expressions:

QA = 5,500 - 200PA QB = 4,500 - 225PB The variable costs per unit of A and B are $18 and

$12, respectively. The weekly production capacity for A and B are 275 and 350 units, respectively.

Each unit of A requires 1 hour of labor, while each unit of B requires 2 hours. There are 700 hours of labor available each week. What quantities and price of products A and B will maximize weekly profit?

( Hint: Set up the objective function in terms of profit per unit multiplied by the number of units produced for both products.) Use several different starting values for the decision variables to try to identify a global optimal solution.