Operations Management: Leather-All line of handmade leather products

Two questions (both questions relate to one another) - Chapter 3 #22 and #23. #22 Leather-All produces a line of handmade leather products. At the present time the company is producing only belts, hand bags and cases. The predicted demand for these three type of items over a six-month planning horizon is as follows: (SEE ATTACHED FOR DATA)

month # of Working Days Belts handbags cases
1 22 2500 1250 240
2 20 2800 680 380
3 19 2000 1625 110
4 24 3400 745 75
5 21 3000 835 126
6 17 1600 375 45

The belts require an average of 2 hours to produce, the handbags 3 hours and the cases 6 hours. All of the workers have the skill to work on any item. Leather-All has 46 employees who each has a share in the firm and cannot be fired. There are an additional 30 locals that are available and can be hired for shoet periods at higher costs. Regular employee = 8.50 / hr and 14.00 / hr on overtime. Regular time comprises a 7 hour work day and regualr employee work as much overtime as is available. The additional workers are hired for $11.00 per hour and are kept on payroll for at least 1 full month. Costs of hiring and firing are negligible. Because of the competitive nature of the industry, Leather-All does not want to incur any demand back orders.

a) using workers hours as an aggregate measure production, convert the forecasted demands to demands in terms of aggregare units.
b) What would be the size of the workforce needed to satisfy the demand for the coming six months on regular time only? Would it be to the Company's advantage to bring the permanent workforce up to this level? Why or why not?
c) Determine a production plan that meets the demand using only regular -time employees and the total cost of that plan.
d) determine a production plan that utilizes only additional employees to absorb excess demand and the cost of that plan.
#23
a) Formulate the problem of optimizing Leather-All's hiring schedule as a linear program. Define all problem variables and include whatever constraints are necessary.
b) Solve the problem formulated in part (a) using a linear programming code. Round all of the relevant variables and determine the cost of the resulting plan. Compare your results with those obtained in Problem 22 (c) & 22 (d).