New Exercise Bank Content Qu$.05-10$New Exercise Bank Content Qu$.05-26$

The Learning Center runs a day camp for $6-$ to $10-$year$-$olds during the summer. Its manager, Elizabeth Reed, is trying to reduce the

center's operating costs to avoid having to raise the tuition fee. Elizabeth is currently planning what to feed the children for lunch. She

would like to keep costs to a minimum, but also wants to make sure she is meeting the nutritional requirements of the children. She

has already decided to go with peanut butter and jelly sandwiches, and some combination of apples, milk, and$/$or cranberry juice. The

nutritional content of each food choice and its cost are given in the table that accompanies this problem. The nutritional requirements

are as follows. Each child should receive between $300$ and $500$ calories, but no more than $30$ percent of these calories should come

from fat. Each child should receive at least $75$ milligrams $(mg)$ of vitamin $C$ and at least $10$grams$(g)$ of fiber. To ensure tasty

sandwiches, Elizabeth wants each child to have a minimum of $2$ slices of bread, $1$ tablespoon $($tbsp$)$ of pea$-$nut butter, and $1tbsp$ of jelly,

along with at least $1$ cup of liquid $($milk and$/$or cranberry juice$).$ Elizabeth would like to select the food choices that would minimize cost

while meeting all these requirements.

Click here for the Excel Data File

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

a$.$ Determine the quantity of diet $($in ounces$)$ for each food choice available. Enter $0$ if food item isn't included.

Note: Round your answers to $2$ decimal places.

Answer is complete but not entirely correct.

b$.$ Determine the total cost.

Note: Round your answer to $2$ decimal places.

Answer is complete and correct.

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. Mark

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 $3,600$ per month. A ${65}^{\text{'}\text{'}}$ set requires $20$ work$-$hours and a ${55}^{\text{'}\text{'}}$ set requires $10$ work$-$hours. Each ${65}^{\text{'}\text{'}}$

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.

Unit Profit

$65$ Sets$55$ Sets

$$270$$$180$

Click here for the Excel Data File

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

a$.$ Determine the number of ${65}^{\text{'}\text{'}}$ and ${55}^{\text{'}\text{'}}$ sets produced if the numbers do not exceed the maxima indicated by the market

research.

b$.$ Determine the total profit.