A Company Makes 2 Products a and B from 2

question 16

Essay

A company makes 2 products A and B from 2 resources. The products have the following resource requirements and produce the accompanying profits. The available quantity of resources is also shown in the table.
$$\begin{array} { l l l c } \text { Product } & 1 & 2 & \text { Available resaurces } \\\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \\\text { Material (aunces/unit) } & 1 & 2 & 200 \\\text { Profit( /unit) } & 7 & 6 &\end{array}$$ Management has developed the following set of goals
Goal 1: Produce approximately 40 urits of product 1
Goal 2: Produce approxinately 70 urits of product 2
Goal 3: Achieve a profit aver $400.
Goal 4: Consume less than 150 hours of labor
Goal 5:Consume lesse than 200 \text ounces of material
Based on the following GP formulation of the problem, and the associated optimal solution, what formulas should go in cells D6:F6, B9:F9, and B16 of the following Excel spreadsheet? NOTE: Formulas are not required in all of these cells.
$\begin{array}{|c|l|c|c|c|c|c|} \hline & {\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \text { Problem Data } & \mathrm{A} & \mathrm{B} & & & \\\hline 2 & \text { Labor } & 3 & 2 & & & \\\hline 3 & \text { Material } & 1 & 2 & & & \\\hline 4 & \text { Profit } & 7 & 6 & & & \\\hline 5 & \text { Goal Constraints } & \mathrm{A} & \mathrm{B} & \text { Labor } & \text { Material } & \text { Profit } \\\hline 6 & \text { Actual Amount } & 4 & 69 & 150 & 142 & 442 \\\hline 7 & + \text { Under } & 36 & 1 & 0 & 58 & 0 \\\hline 8 & - \text { Over } & 0 & 0 & 0 & 0 & 42 \\\hline 9 & =\text { Goal } & 40 & 70 & 150 & 200 & 400 \\\hline 10 & \text { Target Value } & 40 & 70 & 150 & 200 & 400 \\\hline 11 & & & & & & \\\hline 12 & \text { Weights } & & & & & \\\hline 13 & \text { Under } & 1 & 1 & 0 & 0 & 1 \\\hline 14 & \text { Over } & 1 & 1 & 1 & 1 & 0 \\\hline 15 & & & & & & \\\hline 16 & \text { Objective } & 37 & & & & \\\hline\end{array}$

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Definitions:

Figurines

In economics, this term does not carry a specific meaning and is likely referred to collectible or decorative small statues in discussions on consumer behavior or niche markets.

Plastic

A wide range of synthetic or semi-synthetic materials that are malleable and can be molded into solid objects of diverse shapes.

Clay

A natural, earthly material consisting of fine-grained minerals, typically used in the making of ceramics, bricks, and sculptures.

Pounds of Plastic

A unit of measurement denoting the quantity or mass of plastic materials, commonly used in recycling, manufacturing, and environmental studies to gauge plastic use or waste.