A Company Makes Products a and B from 2 Resources

question 50

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. $\begin{array}{lllc}\text { Product } & \text { A } & \text { B } & \text { Available resources } \\\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \\\text { Material (ounces/unit) } & 1 & 2 & 200 \\\text { Manufacturing cost }(\$ / \text { unit) } & 25 & 18 & \\\text { Demand (units) } & 20-0.10^{*} P_{1}& 30-0.07^{*} P_{2} &\end{array}$
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) MAX 25 X₁ + 18 X₂
• B) MAX (20 ? 0.10*P₁) X₁ + (30 ? 0.07*P₂) X₂
• C) MAX 20 P₁ ? 0.1 P₁² + 30 P₂ ? 0.07 P₂² ? 1040
• D) MAX 22.5 P₁ ? 0.1 P₁² + 31.26 P₂ ? 0.07 P₂² ? 1040

---

Definitions:

Mexico

A country in North America, bordered by the United States to the north, and Guatemala and Belize to the south, known for its rich cultural heritage, diverse landscapes, and history.

Slave Trade

The historical trade involving the capture, transport, and sale of human beings as slaves, particularly associated with the transatlantic trade from Africa to the Americas from the 16th to the 19th centuries.

Africans

Refers to the people native to the African continent, encompassing a wide range of cultures, ethnicities, and nations.

Americas

A collective term for the continents of North America and South America, including all its countries and regions.