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:

Utility Function

A mathematical representation that ranks an individual's preferences over a set of goods and services.

Interest Rate

The share of a loan subject to interest charges to the borrower, typically denoted as an annual percentage of the loan's outstanding sum.

Nominal Interest Rate

The stated interest rate on a loan or investment, not adjusted for inflation.

Rational Consumer

An assumption in economics that consumers aim to maximize their utility or satisfaction from consumption choices, given their budget constraints.