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1) Joyce and Marvin are deciding what foods to serve for preschool lunches. They want to minimize costs while meeting nutritional requirements of 400-600 calories with no more than 30% from fat, at least 60mg vitamin C, and 12g protein. They provide a table of nutritional information and costs for various food options. 2) Comfortable Hands makes winter gloves for men, women, and children. They want to decide the mix of gloves to produce weekly to maximize profit. Gloves require different amounts of material and labor. The company has restrictions on full-time and part-time employees due to union contracts. They want to know the optimal glove mix and number of employees.

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244 views1 page

Finals OR

1) Joyce and Marvin are deciding what foods to serve for preschool lunches. They want to minimize costs while meeting nutritional requirements of 400-600 calories with no more than 30% from fat, at least 60mg vitamin C, and 12g protein. They provide a table of nutritional information and costs for various food options. 2) Comfortable Hands makes winter gloves for men, women, and children. They want to decide the mix of gloves to produce weekly to maximize profit. Gloves require different amounts of material and labor. The company has restrictions on full-time and part-time employees due to union contracts. They want to know the optimal glove mix and number of employees.

Uploaded by

jsus22
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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To be submitted at 1 whole yellow paper together with the project.

1) Joyce and Marvin run a day care for preschoolers. They are trying to decide what to feed the children for lunches. They would like
to keep their costs down, but also need to meet the nutritional requirements of the children. They have already decided to go with
peanut butter and jelly sandwiches, and some combination of graham crackers, milk, and orange juice. The nutritional content of
each food choice and its cost are given in the table below.
Calories
Total Vitamin Protein Cost
Food Item from
Calories C (mg) (g) (c)
Fat
Bread
10 70 0 3 5
(1 slice)
Peanut
butter 75 100 0 4 4
(1tbsp)
Strawberry
0 50 3 0 7
jelly (1tbsp)
Graham
cracker 20 60 0 1 8
(1 cracker)
Milk (1 cup) 70 150 2 8 15
Juice (1 cup) 0 100 120 1 35

The nutritional requirements are as follows. Each child should receive between 400 and 600 calories. No more than 30 percent of
the total calories should come from fat. Each child should consume at least 60 milligrams (mg) of vitamin C and 12 grams (g) of
protein. Furthermore, for practical reasons, each child needs exactly 2 slices of bread (to make the sandwich), at least twice as much
peanut butter as jelly, and at least 1 cup of liquid (milk and/or juice).
Joyce and Marvin would like to select the food choices, for each child which minimize cost while meeting the above requirements.

2) Comfortable Hands is a company which features a product line of winter gloves for the entire family – men, women, and children.
They are trying to decide what mix of these three types of gloves to produce.
Comfortable Hands’ manufacturing labor force is unionized. Each full-time employee works a 40-hr a week. In addition, by union
contract, the number of full-time employees can never drop blow 20. Nonunion part-time workers can also be hired with the
following union-imposed restrictions: (1) each part-time worker works 20 hours per week, and (2) there must be at least 2 full-time
employees for each part-time employee.
All three types of gloves are made out of the same 100 percent genuine cowhide leather. Comfortable Hands has a long-term
contract with a supplier of the leather, and receives a 5000 square feet shipment of the material each week. The material
requirements and labor requirements, along with the gross profit per glove sold (not considering labor costs) is given in the following
table.
Glove Material Required Labor Required Gross Profit
(Square Feet) (Minutes) (per Pair)
Men’s 2 30 $8
Women’s 1.5 45 $10
Children’s 1 40 $6
Each full-time employee earns $13 per hour, while each part –time employee earns $13 per hour, while each part-time employee
earns $10 per hour. Management wishes to know what mix of each three types of gloves to produce per week, as well as how many
full-time and how many part-time workers to employ. They would like to maximize their net profit – their gross profit from sales
minus their labor costs.

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