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

question 1

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: $$\begin{array} { | c | c | c | c | } \hline \text { SLACK } & \text { STATUS } & \text { VALUE } & \text { SHADOW PRICE } \\\hline \mathrm { X } 4 & \text { Basic } & 75 & 0 \\\hline \mathrm { X5 } & \text { Non-basic } & 0 & 1.5 \\\hline \mathrm { X6 } & \text { Non-basic } & 0 & .5 \\\hline\end{array}$$

---

Definitions:

Opportunity Cost

The cost of forgoing the next best alternative when making a decision; it represents the benefits that could have been received but were given up to take another course of action.

Medium Of Exchange

A device or mechanism designed to assist in the buying, selling, or exchanging of products among individuals or groups.

American Dollar

The official currency of the United States, also known as the USD or US Dollar.

Members

Individuals who are part of an organization, group, or body, contributing to and benefitting from its activities and objectives.