Formulate and Solve the Following Linear Program

question 1

Essay

Formulate and solve the following linear program.A firm wants to determine how many units of each of two products (products D and E)they should produce to make the most money.The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $87.Although the firm can readily sell any amount of either product,it is limited by its total labor hours and total machine hours available.The total labor hours per week are 4,000.Product D takes 5 hours of labor per unit and product E takes 7 hours of labor per unit.The total machine hours are 5,000 per week.Product D takes 9 hours of machine time per unit and product E takes 3 hours of machine time per unit.Write the constraints and the objective function for this problem,solve for the best mix of product D and E and report the maximum value of the objective function?

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Definitions:

Eliminating Negative Responses

A therapeutic goal or process where negative reactions, behaviors, or emotions are reduced or removed, often through techniques like counter-conditioning or cognitive-behavioral therapy.

Contingency Management

A behavior modification technique where certain behaviors are reinforced by rewards or punishments.

Positive Reinforcement

A behavioral strategy employing rewards or positive outcomes to increase the likelihood of a desired behavior being repeated.

Antecedent

An event, condition, or stimulus that precedes a behavior and may influence or trigger the behavior to occur.