Exhibit 81
the Following Questions Pertain to the Problem and Spreadsheet

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
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 25 to make and demand is estimated to be 20 ? .10 * Price of A.A unit of B costs 18 to make and demand is estimated to be 30 ? .07 * 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 100 and 200.
$\begin{array}{lccc}\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \\\hline \text { Labor hr/unit) } & 3 & 2 & 150 \\\text { Material ounces/unit) } & 1 & 2 & 200 \\\text { Manufacturing cost\$/unit) } & 25 & 18 & \\\text { Demand units) } & 20-.10^{*} \mathrm{P}_{1} & 30-.07^{*} \mathrm{P}_{2} &\end{array}$
Let X₁ = demand for As and X₂ = demand for Bs.Let P₁ = price for As and P₂ = price for Bs

-How much must the objective function coefficient of the variable Pumpkin change before any Pumpkins are
Produced based on the following sensitivity report?
Changing Cells
Final Reduced
Cell Name Value Gradient
$B$4 Corn 9.52 0
$C$4 Pumpkin 0 ?499.99
$D$4 Beans 10.79 0
Constraints
Final Lagrange
Cell Name Value Multiplier
$E$8 Corn 200000.00 0.016
$E$9 Pumpkin 99.00 12.000
$E$10 Beans 37777.78 0
$E$11 Water 29.84 0
$E$12 Fertilizer 8000.00 3.490

A) increase by 12
B) decrease by 12
C) increase by 499.99
D) decrease by 499.99