Linear Programming Problem?
Comfortable Hands is a company that 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.
The company’s labour force is unionized. Each full-time employee works a 40-hour week. By union contract, the number of full-time employees can never drop below 20. Non-union part-time workers can also be hired with the following restrictions:
(i) Each part-time worker works 20 hours per week.
(ii) 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 genuine cowhide leather. Comfortable Hands has a long-term contract with a leather supplier and receives a 5000 ft2 shipment of the material each week. The material and labour requirements along with the gross profit per glove sold are given in the following table.
Glove Material (ft2) Labour required (minutes) Gross profit 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 £10 per hour.
The company would like to determine the mix of gloves to produce per week and how many full-time and part-time workers to employ in order to maximize their net profit.
produce 2,480 Mens Gloves only. Employ, 25 Full Timers, and 12 Part Timers, Giving a Gross Profit of 19840 and a Net Profit of 4440. Is this correct? Because my teacher is a crafty buggar and i know he wouldnt distribute the whole manufacture to JUST Mens Gloves. Leading me to think i have gone wrong somewhere.