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Question: What is an Estimate the optimal production plan and run the sensitivity analysis. Analyze the tac...

What is an Estimate the optimal production plan and run the sensitivity analysis. Analyze the tactical and strategic information provided by the optimal solution:

1. Optimal output plan for the company?
2. What factors could lead to even better level of performance:
   1. For each department, what is the marginal value of additional overtime capacity?
   2. What is the marginal value of additional advertising dollars?
   3. What is the marginal value of additional sales for each product?
3. What is the trade-off between advertising expenditures and increased sales for Hawley Co. if the advertising budget is to be increased? How would the increase affect the production plan? Assume an increase in the advertising budget by the amount of the allowable increase - how does this advertising budget change affect the optimal production plan?

The Hawley Lighting Company manufactures four types of lamps at its factory including table lamps, floor lamps, ceiling lamps, and pendant lamps. Table 1 presents the average material costs for each of the products. 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 are shown in Table 2. The capacities are measured in units of product. Note that there are regular and overtime possibilities for each department. Average selling prices for the four products are known, and estimates have been made of the market demand for each product at these prices (see Table 3). 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 than $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. Table 1 Product Table Floor Ceiling Pendant Material cost $66 85 50 80 Table 2 Regular Time Overtime Process Unit Cost Capacity 100,000 Unit Cost 18 $16 Department 1 Department 2 Capacity 25,000 24,000 12 90,000 15 Table 3 Floor 150 Ceiling 100 Selling price Potential sales (000) Advertising effect Table $120 60 12% Pendant 160 35 15% 20 100 10% 8% 1 Costs and prices: B C D E F G H I r=regular time; o = overtime Table lamps (T) Floor lamps (F) | Ceiling lamps (C) Pendant lamps (P) | Tr To Fr Fo CrCo Pr Po 120 120 150 150 100 100 160 160 66 85 85 50 50 80 80 16 18 16 18 12 15 12 15 36 49 47 38 35 68 65 Department 1 Department 2 5 Celling price 6 Material costs 7 Production costs 8 Unit profit 10 11 Decision Variables: 12 13 Units produced To Fo Po Tr 67,200 Fr 20,000 ] 0 Cr 50800 C o 24000 Pr 39200 0 0 14 10,000 0 0 8000 8969600 20 LHS 87,200 15 Advertising 16 17 Objective function: 19 max (Profit) = 21 Constraints: 22 Capacity constraints: 23 Department 1 regular time 24 Department 1 overtime 25 Department 2 regular time 26 Department 2 overtime 27 Demand constraints: 28 Table lamps 29 Floor lamps 30 Ceiling lamps 31 Pendant lamps 32 33 Advertising constraint 34 RHS 100000 25000 90000 24000 90,000 24,000 67,200 20,000 74,800 39,200 67200 20000 100000 39200 18,000 18000 The Hawley Lighting Company manufactures four types of lamps at its factory including table lamps, floor lamps, ceiling lamps, and pendant lamps. Table 1 presents the average material costs for each of the products. 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 are shown in Table 2. The capacities are measured in units of product. Note that there are regular and overtime possibilities for each department. Average selling prices for the four products are known, and estimates have been made of the market demand for each product at these prices (see Table 3). 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 than $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. Table 1 Product Table Floor Ceiling Pendant Material cost $66 85 50 80 Table 2 Regular Time Overtime Process Unit Cost Capacity 100,000 Unit Cost 18 $16 Department 1 Department 2 Capacity 25,000 24,000 12 90,000 15 Table 3 Floor 150 Ceiling 100 Selling price Potential sales (000) Advertising effect Table $120 60 12% Pendant 160 35 15% 20 100 10% 8% 1 Costs and prices: B C D E F G H I r=regular time; o = overtime Table lamps (T) Floor lamps (F) | Ceiling lamps (C) Pendant lamps (P) | Tr To Fr Fo CrCo Pr Po 120 120 150 150 100 100 160 160 66 85 85 50 50 80 80 16 18 16 18 12 15 12 15 36 49 47 38 35 68 65 Department 1 Department 2 5 Celling price 6 Material costs 7 Production costs 8 Unit profit 10 11 Decision Variables: 12 13 Units produced To Fo Po Tr 67,200 Fr 20,000 ] 0 Cr 50800 C o 24000 Pr 39200 0 0 14 10,000 0 0 8000 8969600 20 LHS 87,200 15 Advertising 16 17 Objective function: 19 max (Profit) = 21 Constraints: 22 Capacity constraints: 23 Department 1 regular time 24 Department 1 overtime 25 Department 2 regular time 26 Department 2 overtime 27 Demand constraints: 28 Table lamps 29 Floor lamps 30 Ceiling lamps 31 Pendant lamps 32 33 Advertising constraint 34 RHS 100000 25000 90000 24000 90,000 24,000 67,200 20,000 74,800 39,200 67200 20000 100000 39200 18,000 18000