Question: Leather-All produces a line of handmade leather products. At the present time, the company is producing only belts, handbags, and attaché cases. The predicted demand for these three types of items over a six-month planning horizon is as follows:
The belts require an average of two hours to produce, the handbags three hours, and the attaché cases six hours. All 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 short periods at 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 back orders.
a. Using worker hours as an aggregate measure of production, convert the forecasted demands to demands in terms of aggregate 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. Formulate the problem of optimizing Leather-All's hiring schedule as a linear program. Define all problem variables and include whatever constraints are necessary.
d. Solve the problem formulated in part (a) for the optimal solution. Round all the relevant variables and determine the cost of the resulting plan.