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:

Qualitative Forecasting

A forecasting method that relies on expert judgment and historical data analysis rather than quantifiable metrics, often used when precise data is unavailable.

Expert Opinions

Insights and assessments provided by individuals with extensive knowledge and experience in a specific field.

Internal Benchmarking

The process of comparing business processes and performance metrics to industry bests or best practices within the same organization.

Work Units

Small divisions or groups within an organization that focus on specific tasks or projects.