Optimization: Coordinating Advertising and Production

The Hawley Lighting Company manufactures four families of household lighting at its factory. The product families are table lamps, floor lamps, ceiling fixtures, and pendant lamps. The following table shows the average material costs for each of the products.

Product Table Floor Ceiling Pendant
Material Cost $66 $85 $50 $80

Each product is made in one of two production processes by purchasing components, assembling and testing the product, and finally packaging it for shipping. Table lamps and floor lamps go through the assembly and finishing process in Department 1, while ceiling fixtures and pendant lamps go through the process in Department 2. Variable production costs and capacities (measured in units of product) are shown in the following table. The capacities are measure in units of product. Note that there are regular and overtime possibilities for each department.

Regular Time Overtime
Process Unit Cost Capacity Unit Cost Capacity
Department 1 $16 100,000 $18 25,000
Department 2 $12 90,000 $15 24,000

Average selling prices for the four products are known, and estimates have been made of the market demand for each product at these prices. These figures are shown in the following table.

Table Floor Ceiling Pendant
Selling Price $120 $150 $100 $160
Potential Sales (000) 60 20 100 35
Advertising Effect 12% 10% 8% 15%

Sales levels can also be affected by advertising expenditures. Starting with the demand levels in the table, an increase of up to $10,000 in advertising raises the demand by the percentage shown in the last row. An expenditure of less tan $10,000 in advertising will lead to a proportional effect on demand. For example, an increase in advertising of $5,000 for table lamps would raise demand by 6 percent, or 3,600 units. However, there is a budget limit of $18,000 on the total amount to be spent on advertising among all four products.

a. What is an optimal output plan for the company?
b. For each department, what is the marginal value of additional overtime capacity?
c. What is the marginal value of additional advertising dollars?
d. What is the marginal value of additional sales for each product?