Give the Mathematical Formulation of the Linear Programming Problem

question 3

Essay

Give the mathematical formulation of the linear programming problem. Graph the feasible region described by the
constraints and find the corner points. Do not attempt to solve.
-A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The monthly salary
of a counselor is $2400 and the monthly salary of an aide is $1100. The camp can accommodate up to 45 staff
members and needs at least 30 to run properly. They must have at least 10 aides, and at most twice as many
aides as counselors. How many counselors and how many aides should the camp hire to minimize cost?

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Definitions:

Efficient Level

The point at which a system or operation is performing at its maximum potential without wasting resources.

Megawatts

A unit of power measurement equal to one million watts, commonly used to express the output of large power plants or the amount of electrical energy used by large entities.

Consumer Surplus

The difference between the total amount consumers are willing and able to pay for a good or service and the total amount they actually do pay.

Producer Surplus

The difference between what producers are willing and able to sell a product for and the actual price they receive, indicating the benefit to producers.