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

Question 49

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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.
 Product  A  B  Avalable resources  Labor hr/unit) 24150 Material ounces/unit) 28220 Manufacturing cost$/unit) 3020 Demand units) 500.09P13014P2\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:
 MAX: 52.70P10.09P12+32.80P20.14P222100 Subject to: X150+0.09P1=0X230+0.14P2=02X1+4X21502X1+8X222090P1,P2140X1,X20 and the solution P1,P2)=140.0,117.14)\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?
 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 X<sub>1 </sub>= demand for As and X<sub>2 </sub>= demand for Bs.Let P<sub>1 </sub>= price for As and P<sub>2 </sub>= 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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