Note: This Problem Requires Excel Use Separable Programming to Find the Optimal Production Plan

Multiple Choice

Note: This problem requires Excel.
A firm offers two different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $75 each for the first 25 units and $60 for each unit over 25. Product 2's profitability is $200 each for the first 50 units and $100 each for each unit over 50. The products each require two raw materials to produce (see table below for usages and available quantities) .
$$\begin{array} { | c | r | r | r | } \hline\begin{array} { c } \text { Raw } \\\text { Material }\end{array} & \begin{array} { c } \text { Praduct l usage } \\\text { (gallons per unit) }\end{array} & \begin{array} { c } \text { Praduct 2 usage } \\\text { (gallons per unit) }\end{array} & { \begin{array} { c } \text { Available Quantity } \\\text { (gallons) }\end{array} } \\\hline \text { A } & 10 & 20 & 1,500 \\\hline \text { B } & 5 & 7 & 2,000 \\\hline\end{array}$$
Use separable programming to find the optimal production plan.

A) 100 units Product 1, 100 units Product 2
B) 50 units Product 1, 50 units Product 2
C) 100 units Product 1, 25 units Product 2
D) 25 units Product 1, 100 units Product 2
E) 100 units Product 1, 50 units Product 2