gncering Midterm Test, October 26, 2017 Thursday (Closed book and notes) Name Ba
ID: 367352 • Letter: G
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gncering Midterm Test, October 26, 2017 Thursday (Closed book and notes) Name Bala knshn Scores Show all your work leading to the solutions. Work quickly but with care. Show essential steps and formulas for "partial credit,” and please use answer spaces where provided. 4 questions in total of 100 pts. 1. Comfortable Hands is a company which features a product line of winter gloves for the entire family-men, Comfortable Hands' manufacturing labor force is unionized. Each full-time employee works a 40-hour week. In addition, by union contract, the number of full-time employees can never drop below 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 % genuine cowhide leather. Comfortable Hands has a long term contract with a supplier of the leather, and receives a 5,000 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. Material Required Labor Required Gross Profit Glove Men's Women's Children's (square feet) minutes 30 45 40 $8 $10 $6 1.5 Each full-time employee earns $13 per hour, while each part-time employee earns $10 per hour. Management wishes to know what mix of each of the 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. Formulate a linear programming model for this problem Conly formulation, not to solve for solution) The decision variables can be denoted and defined as follows: M number of men's gloves to produce per week, W- number of women's gloves to produce per week, number of children's gloves to produce per week, F number of full-time workers to employ, PT- number of part-time workers to employExplanation / Answer
Letting
M = number of men’s gloves to produce per week,
W = number of women’s gloves to produce per week,
C = number of children’s gloves to produce per week,
F = number of full-time workers to employ, and
P = number of part-time workers to employ,
formulate a linear programming model for this problem, and put it into standard form (with only £ constraints).
Max Z= 8M + 10W + 6C – 13(40)F – 10(20)P,
S.T
2 M + 1.5 W + C 5000
30 M + 45 W + 40 C 40(60) F + 20(60) P
F 20 or –F -20
F 2P or –F + 2P 0
M , W , C , F , P0.
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