Note: This problem requires Excel.
A firm offers three 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: $10 each for the first 50 units, $9 each for units 51-100, and $8 for each unit over 100. Product 2's profitability is $20 each for the first 25 units, $19 each for units 26-50, and $18 each for each unit over 50. The products each require 3 raw materials to produce (see table below for usages and available quantities).
$\begin{array}{|c|r|r|r|}
\hline
\begin{array}{c}
\text { Raw } \
\text { Material }
\end{array} & \begin{array}{c}
\text { Product 1 usage } \
\text { (pounds per unit) }
\end{array} & \begin{array}{c}
\text { Product 2 usage } \
\text { (pounds per unit) }
\end{array} & \begin{array}{c}
\text { Available Quantity } \
\text { (pounds) }
\end{array} \
\hline \text { A } & 5 & 12 & 1,000 \
\hline \text { B } & 4 & 10 & 2,000 \
\hline \text { C } & 7 & 6 & 1,500 \
\hline
\end{array}$
Use separable programming to find the optimal production plan.
A) 100 units Product 1, 100 units Product 2
B) 100 units Product 1, 50 units Product 2
C) 140 units Product 1, 25 units Product 2
D) 25 units Product 1, 140 units Product 2
E) 100 units Product 1, 140 units Product 2

Question

Quizplus · Accepted Answer

The optimal production plan maximizes profit while adhering to the constraints of raw material availability. By calculating the profit per unit and considering the raw material constraints, it's determined that producing 140 units of Product 1 and 25 units of Product 2 utilizes the available resources most efficiently and yields the highest profit.

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