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

question 3

Multiple Choice

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 product A costs 25 to make and demand is estimated to be 20 ?
) 10 * Price of A.A unit of product 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.
$\begin{array}{lccc}\text { Product } & \text { A } & \text { B } & \text { Available resources } \\\hline \text { Labor hr/unit) } & 3 & 2 & 150 \\\text { Material ounces/unit) } & 1 & 2 & 200 \\\text { Manufacturing cost\$/unit) } & 25 & 18 & \\\text { Demand units) } & 20- & 30- & \\& 0.10^{*} \mathrm{P} 1 & 0.07^{*} \mathrm{P}_{2} &\end{array}$

Let X₁ = demand for As and X₂ = demand for Bs.Let P₁ = price for As and P₂ = price for Bs.
The objective function for this problem is?

• A)\(\operatorname { MAX } 25 X _ { 1 } + 18 X _ { 2 }\)
• B)\(\left. \left. \operatorname { MAX } 20- 0.1 0 ^ { * } \mathrm { p } _ { 1 } \right) \mathbf { X } _ { 1 } + 3 0- 0.07* \mathrm { p } _ { 2 } \right) \mathbf { X } _ { \mathbf { 2 } }\)
• C)\(\operatorname{MAX} 20 P_{1}-0.1 P_{1}^{2}+30 P_{2}-0.07 P_{2}^{2}-1040\)
• D)\(\operatorname{MAX} 22.5 P_{1}-0.1 P_{1}^{2}+31.26 P_{2}-0.07 P_{2}^{2}-1040\)

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Definitions:

Direct Materials

Raw materials that can be directly attributed to the production process of a product and are clearly identified as part of the finished product.

Manufacturing Overhead

All manufacturing costs that are not directly involved in the production process, such as maintenance, supervision, and utilities.

Operating Expenses

Costs related to the normal operations of a business, such as salaries, rent, and utilities, but excluding cost of goods sold.

Property Taxes

Taxes assessed on real estate by the government, typically based on the property's value.