A Company Makes Products a and B from 2 Resources

Essay

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 A costs 30 to make and demand is estimated to be 50  .09 * Price of A. A unit of B costs 20 to make and demand is estimated to be 30  .14 * 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 90 and 140.
$\begin{array}{lllc}\text { Product } & \text { A } & \text { B } & \text { Available resources } \\\hline \text { Labor (hr/unit) } & 2 & 4 & 150 \\\text { Material (ounces/unit) } & 2 & 8 & 220 \\\text { Manufacturing cost(\$/unit) } & 30 & 20 & \\\text { Demand (units) } & 50-0.09 * P_{1} & 30-0.14 * P_{2} &\end{array}$
Let X₁ = demand for As and X₂ = demand for Bs.
Let P₁ = price for As and P₂ = price for Bs.
Formulate the NLP for this company