A Company Makes Products a and B from 2 Resources

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. $\begin{array}{lllc}\text { Product } & \text { A } & \text { B } & \text { Available resources } \\\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \\\text { Material (ounces/unit) } & 1 & 2 & 200 \\\text { Manufacturing cost }(\$ / \text { unit) } & 25 & 18 & \\\text { Demand (units) } & 20-0.10^{*} P_{1}& 30-0.07^{*} P_{2} &\end{array}$
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

Correct Answer:

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