1) Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion, Michigan. Based on orders received and forecasts of buying habits, it is estimated that the demand for the next four months is 850, 1260, 510 and 980, expressed in thousands of cookies. During a 46-day period when there were 120 workers, the company produced 1.7 million cookies. Assume that the number of workdays over the four months are respectively 26, 24, 20 and 16. There are currently 100 workers employed, and there is no starting inventory of cookies.
a) What is the minimum constant workforce required to meet demand over the next four months?
b) Assume that CI= 10 cents per cookie per month, CH =$100, and Cf = $200. Evaluate the cost of the plan derived in part (a).
2) A local firm manufactures children's toys. The projected demand over the next four months for one particular model of toy robot is:
|
month
|
Work days
|
Forecasted demand(in agg units)
|
|
july
|
23
|
3,825
|
|
aug
|
16
|
7,245
|
|
sep
|
20
|
2770
|
|
oct
|
22
|
4440
|
Assume that a normal work day is eight hours. Hiring costs are $350 per worker and firing costs (including severe pay) are $850 per worker. Holding costs are $4.00 per aggregate unit held per month. Assume that it requires an average of 1 hour and 40 minutes for one worker to assemble one toy. Shortages are not permitted. Assume that the ending inventory for June was 600 of these toys and the manager wishes to have at least 800 units on hand at the end of October. Assume that the current workforce level is 35 workers. Find the optimal plan by formulating as a linear program.