Project Question A cheese fim produces two types of cheese: Swiss cheese and sha
ID: 3184197 • Letter: P
Question
Project Question A cheese fim produces two types of cheese: Swiss cheese and sharp cheese. The firm has 60 experienced workers and would like to increase its workforce to at least 90 workers during the next 8 weeks. Each experienced worker can train 1 - 3 new employees in a period of two weeks during which the experienced and new workers involved virtually produce nothing. After the training period of two weeks, new employees become experienced workers and can produce cheese The production rate of Swiss cheese is 10 pounds per worker per hour, and the production rate of sharp cheese is 8 pounds per worker per hour. Each worker works at most 40 hours per week. The weekly demands (in 1000 pounds) are summarized in the table below. Since overaging destroys the flavor of the cheese, the cheese produced in each week can be sold only in the current and next weeks. For example, the cheese produced in week 1 can be sold in weeks 1 and 2. Usually, unsold cheese is donated to food banks. There is no cheese in inventory at the beginning of week 1 Weekly demands of each type of cheese (in 1000 pounds) Cheese Type Swiss cheese Sharp cheese Week 1 Week 3 13 10 Week 4 18 12 Week 5 14 12 Week 6 18 13 Week 7 20 16 Week 2 Week 8 12 18 Suppose that a trainee receives the same full salary as an experienced worker. How should the company hire and train its new employees so that the labor cost is minimized over this 8-week period and all demands are met? Project Requirements (1) Formulate the problem as an LP or ILP model, and then use What'sBest to solve it. (2) Write a project report that explains how you formulate the problem, presents your LP or ILP model, and reports and interpret the optimal training plan found using What'sBest.Explanation / Answer
We need to decide the amount of time allotted over to the workers to train new staff (as we, certainly, will not make use of all the available working time) and also to decide the total number of trainings completed. Hence let:
xi = number of weeks allotted to train the work force i (i=1,2,3,…8)
y = number of trained work force
where xi >= 0 i=1,2,3….8 and y >= 0 and (as is usual) we assume that any fractional parts in the variables in the numerical solution of the LP are not significant.
Currently 60 workers work for 40 hours each. i.e., 2400 hours per week. Assuming 30 workers produce Swiss Cheese and other 30 produce sharp cheese, for 1200 hours, they produce, 12000 pounds of swiss cheese and for other 1200 hours, they produce, 7200 pounds of sharp cheese.
Constraints:
o x2 <= 1200 hours of sharp cheese
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.