A Company Manufactures 50-Inch and 75-Inch Rear Projection Television Sets

question 10

Essay

A company manufactures 50-inch and 75-inch rear projection television sets. Each 50-inch set contributes $200 to profits and each 75-inch set contributes $475 to profits. The company has purchase commitments for 500 50-inch sets and 200 75-inch sets for the next month, so they want to make at least that many television sets. Although they think they can sell all the 50-inch sets that they could currently make, they do not think they can sell more than 375 75-inch sets. Their production capacity allows them to make only 975 sets in total including both types of television sets. They want to know how many of each type to make so as to maximize profits.
a. What is the objective function for this LP problem?
b. What are the constraints involving x₁, assuming that x₁ corresponds to 50-inch TV sets?
c. What is the optimal solution point for this problem?
d. What is the optimal value of the objective function?

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Definitions:

Oxygen Uptake

Oxygen uptake is a measure of the oxygen used by the body during physical activity and is a key indicator of aerobic fitness.

Mean Difference

A statistical measure representing the average difference between two sets of values or groups within a dataset.

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

P-value

The probability of observing a test statistic at least as extreme as the one observed, under the assumption that the null hypothesis is true.