A Small Firm Makes Three Products, Which All Follow the Same

Essay

A small firm makes three products, which all follow the same three-step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit.
Use the following computer output to find the optimum mix of products in terms of maximizing contributions to profits for the next period.
PROBLEM TITLE: LINEAR PROGRAMMING
PROBLEM IS A MAX WITH 3 VARIABLES AND 3 CONSTRAINTS. $$\begin{array} { | l | l | l | l | l | } \hline \text { ROW } & \text { X1 } & \text { X2 } & \text { X3 } & \text { RHS } \\\hline\end{array}$$ $$\begin{array} { | l | l | l | l | } \hline \text { COST } & 6.00 & 4.00 & 10.00 \\\hline\end{array}$$ $$\begin{array} { | l | l | l | l | l | r | } \hline 1 - & 6.00 & 2.50 & 5.00 & \leq & 1,200.00 \\\hline 2 - & 5.00 & 2.00 & 4.00 & \leq & 900.00 \\\hline 3 - & 4.00 & 2.00 & 8.00 & \leq & 1,440.00 \\\hline\end{array}$$ NUMBER OF ITERATIONS: 2
OPTIMAL SOLUTION:
OBJECTIVE FUNCTION VALUE = 2,070
DECISION VARIABLE SECTION: $$\begin{array} { | c | c | c | c | } \hline \text { VARIABLE } & \text { STATUS } & \text { VALUE } & \text { REDUCED COST } \\\hline \mathrm { X } 1 & \text { Non-basic } & 0 & 3.5 \\\hline \mathrm { X } 2 & \text { Basic } & 180 & 0 \\\hline \mathrm { X } 3 & \text { Basic } & 135 & 0 \\\hline\end{array}$$ SLACK VARIABLES SECTION: $$\begin{array} { | c | c | c | c | } \hline \text { SLACK } & \text { STATUS } & \text { VALUE } & \text { SHADOW PRICE } \\\hline \mathrm { X } 4 & \text { Basic } & 75 & 0 \\\hline \mathrm { X5 } & \text { Non-basic } & 0 & 1.5 \\\hline \mathrm { X6 } & \text { Non-basic } & 0 & .5 \\\hline\end{array}$$