A Company Makes Products a and B from 2 Resources

question 23

Essay

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. 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: What values should go in cells B3:E18 of the spreadsheet for this problem?

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Definitions:

Plane Crash

An event wherein an aircraft sustains such damage from an in-flight incident that it is unable to continue flight, often leading to injury or loss of life.

Coin Flips

A simple probabilistic experiment to demonstrate the concept of randomness and chance, often used to illustrate the principle of a 50/50 chance in binary outcomes.

Addition Rule

A principle in probability stating that the probability of the occurrence of at least one of two events is the sum of their individual probabilities, minus the probability of both occurring together.

Possible Outcomes

The set of all distinct outcomes that can result from a particular statistical experiment or random event.