A Company Makes Products a and B from 2 Resources,labor

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

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) $\operatorname { MAX } 25 X _ { 1 } + 18 X _ { 2 }$
B) $\left. \left. \operatorname { MAX } 20- 0.1 0 ^ { * } \mathrm { p } _ { 1 } \right) \mathbf { X } _ { 1 } + 3 0- 0.07* \mathrm { p } _ { 2 } \right) \mathbf { X } _ { \mathbf { 2 } }$
C) $\operatorname{MAX} 20 P_{1}-0.1 P_{1}^{2}+30 P_{2}-0.07 P_{2}^{2}-1040$
D) $\operatorname{MAX} 22.5 P_{1}-0.1 P_{1}^{2}+31.26 P_{2}-0.07 P_{2}^{2}-1040$