A Manager Must Decide on the Mix of Products to Produce

question 66

Essay

A manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute for packing. Product B requires two minutes per unit for molding, four minutes for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have contributions of $1.50 per unit. Answer the following questions; base your work on the solution panel provided.
$\begin{array}{|r|r|r|r|r|r|} \hline& \text { A } & \text { B } & &\text { RHS } & \text { Dual } \\\hline \text { Maximize } & 1.5 & 1.5 & \Leftarrow & & \\\hline \text { Molding } & 3. & 2 . & \Leftarrow & 600 & 0.375 \\\hline \text { Painting } & 2. & 4. & \Leftarrow & 600 & 0.1875 \\\hline \text { Packing } & 1. & 3 . & \Leftarrow & 420 & 0. \\\hline \text { Solution }--> & 150 & 75 & & 337.5 &\\\hline\end{array}$
a. What combination of A and B will maximize contribution?
b. What is the maximum possible contribution?
c. Are any resources not fully used up?
Explain.

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Definitions:

Better Technology

Improvements or advancements in technology that increase efficiency or productivity.

Concave Production Possibilities Curve

A graphical representation indicating increasing opportunity costs as more of one good is produced, resulting in a bowed-out shape.

Economic Resources

These are the assets, materials, and inputs used to produce goods and services, including labor, capital, and natural resources.

Opportunity Costs

The value of the foregone alternative when a decision is made; essentially, the cost of choosing one option over another.