A Company Makes Products a and B from 2 Resources,labor

question 25

Essay

A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of A costs 30 to make and demand is estimated to be 50 ? 0.09 * Price of A.A unit of B costs 20 to make and demand is estimated to be 30 ? 0.14 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 90 and 140.
$\begin{array}{lrrr}\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \\\hline \text { Labor hr/unit) } & 2 & 4 & 150 \\\text { Material ounces/unit) } & 2 & 8 & 220 \\\text { Manufacturing cost\$/unit) } & 30 & 20 & \\\text { Demand units) } & 50-0.09^{*} \mathrm{P}_{1} & 30-14^{*} \mathrm{P}_{2} &\end{array}$
Let X₁ = demand for As and X₂ = demand for Bs.Let P₁ = price for As and P₂ = price for Bs.
The NLP for the problem is:
$\begin{array}{ll}\text { MAX: } & 52.70 \mathrm{P}_{1}-0.09 \mathrm{P}_{1}{ }^{2}+32.80 \mathrm{P}_{2}-0.14 \mathrm{P}_{2}{ }^{2}-2100 \\\text { Subject to: } & \mathrm{X}_{1}-50+0.09 \mathrm{P}_{1}=0 \\& \mathrm{X}_{2}-30+0.14 \mathrm{P}_{2}=0 \\& 2 \mathrm{X}_{1}+4 \mathrm{X}_{2} \leq 150 \\& 2 \mathrm{X}_{1}+8 \mathrm{X}_{2} \leq 220 \\& 90 \leq \mathrm{P}_{1}, \mathrm{P}_{2} \leq 140 \\& \mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \\& \text { and the solution } \left.\left.\mathrm{P}_{1}, \mathrm{P}_{2}\right)=140.0,117.14\right)\end{array}$
What values should go in cells B3:E18 of the spreadsheet for this problem?

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Definitions:

Northern Financiers

Refers to the wealthy bankers and investors located in the Northern United States, particularly influential during the 19th and early 20th centuries, often associated with industrial growth and the financing of wars and infrastructure.

South

Typically refers to the southeastern and south-central regions of the United States, characterized by its unique history, culture, and social issues.

Fifteenth Amendment

An amendment to the U.S. Constitution ratified in 1870, granting African American men the right to vote by stating that the right to vote cannot be denied based on "race, color, or previous condition of servitude."