New Exercise Bank Content Qu$.05-10$

The Apex Television Company has to decide on the number of ${65}^{\text{'}\text{'}}$ and ${55}^{\text{'}\text{'}}$ sets to be produced at one of its factories. Market

research indicates that at most $280$ of the ${65}^{\text{'}\text{'}}$ sets and $70$ of the ${55}^{\text{'}\text{'}}$ sets can be sold per month. The maximum number of work$-$

hours available is $3,800$ per month. A ${65}^{\text{'}\text{'}}$ set requires $20$ work$-$hours and a ${55}^{\text{'}\text{'}}$ set requires $10$ work$-$hours. Each $65"$ set sold

produces a profit of $$270$ and each ${55}^{\text{'}\text{'}}$ set produces a profit of $$180.$ A wholesaler has agreed to purchase all the television sets

produced if the numbers do not exceed the maxima indicated by the market research.

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Formulate and solve a linear programming model for this problem on a spreadsheet.

a$.$ Determine the number of $65"$ and $55"$ sets produced if the numbers do not exceed the maxima indicated by the market research.

b$.$ Determine the total profit.