Leather-All produces a line of handmade leather products. At the present time, the company is producing only belts, handbags, and attache cases. The predicted demand for these three types of items over a six-month planning horizon is as follows:

Month No. of Belts Handbags Attache Cases
Working days
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 two hours to produce, the handbags three hours, and the attache cases six hours; all the workers have the skill to work on any item. Leather-All has 46 employees who each have a share in the firm and cannot be fired. There are an additional 30 locals that are available and can be hired for short periods at a higher cost. Regular employees earn $8.50 per hour on regular time, and $14.00 per hour on overtime. Regular time comprises a seven-hour workday and the regular employees will work as much overtime as is available. The additional workers are hired for $11.00 per hour and are kept on the payroll for at least one 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 backorders.

(a) Using worker hours as an aggregate measure of production, convert the forecasted demand to demand in terms of aggregate units.

(b) What would be the size of the work force 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 work force 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.

(e) Formulate the problem of optimizing Leather-All's hiring schedule as a linear program. Define all variables and include the necessary constraints.