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:

Faculty Evaluation

The assessment process of teachers and professors based on performance, effectiveness in teaching, research contributions, and other professional activities.

Teaching Evaluations

Formal assessments of an instructor's teaching performance, often completed by students, used to improve teaching methods and academic offerings.

Peer Evaluations

An assessment process where individuals assess the performance or work of their colleagues at a similar level.

Self-Fulfilling Prophecy

A belief or expectation that influences actions in a way that causes the belief to come true, thereby validating the original expectation.