Can you solve this problem using linear programming and excel solver??

4. 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 the 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 chandeliers go through the processes in Department 2. Variable production costs and capacities (measured in units of product) are shown in the following table. Note that there are regular and overtime possibilities for each department. Regular Time Process Unit Cost Capacity Department 1 $16 100,000 Department 2 $12 190,000 Overtime Unit Cost Capacity $18 25,000 $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: Product Table Floor Ceiling Pendant Selling Price $120 $150 $100 $160 Potential Sales 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 percent shown in the last row. 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 the 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