A Company Makes Products a and B from 2 Resources

Multiple Choice

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.
Let X₁ = demand for As and X₂ = demand for Bs.
Let P₁ = price for As and P₂ = price for Bs.
The objective function for this problem is?

A) MAX 25 X₁ + 18 X₂
B) MAX (20 -0.10*P₁) X₁ + (30 - 0.07*P₂) X₂
C) MAX 20 P₁ - 0.1 P₁² + 30 P₂ - 0.07 P₂² - 1040
D) MAX 22.5 P₁ - 0.1 P₁² + 31.26 P₂ - 0.07 P₂² - 1040