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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