A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of product A costs 25 to make and demand is estimated to be 20 - .10 * Price of A. A unit of product B costs 18 to make and demand is estimated to be 30 - .07 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 100 and 200.
Product
|
A
|
B
|
Available resources
|
Labor (hr/unit)
|
3
|
2
|
150
|
Material (ounces/unit)
|
1
|
2
|
200
|
Manufacturing cost($/unit)
|
25
|
18
|
|
Demand (units)
|
20 - 0.10*P1
|
30 - 0.07*P2
|
|
Let X1 = demand for As and X2 = demand for Bs.
Let P1 = price for As and P2 = price for Bs.
What is the objective function for this problem?