A chemical manufacturing company produces three types of industrial solvents, S-1,S-2, and S-3. The profits per thousand gallons for the three solvents are $300, $500, and $800 respectively. The production process requires blending and purification. It also requires additional labor for handling the finished products. The company has 260 hours of blending, 300 hours of purification, and 160 labor hours available. The requirements for each solvent are shown in the table below:
S-1 S-2 S-3
Blending (hours/1000gallons)
2 2 3
Purification (hours/1000gallons)
1 2 4
Labor (hours/1000gallons)
1 2 2
1. Formulate a linear program that can be used to determine the optimal product mix for the chemical company. Specifically, do the following: Identify the decision variables (make sure that you specify the units for these variables). Specify the objective function and the relevant constraints.
2. The production manager uses a DSS to obtain the optimal production mix. For this optimal product mix, 250 hours of blending, 300 hours of purification, and 160 hours of labor are required. The maximum attainable profit is desired. Develop a simple DSS prototype to solve this production planning problem and to confirm the optimal solutions.
a. How many gallons of S-1, S-2, and S-3 are produced under this optimal product mix?
b. What is the maximum attainable profit?
c. What is the profit contribution for each solvent (S-1, S-2, S-3)?
3. Perform sensitivity analysis to determine how much should the manager be willing to pay for:
(a) an additional hour of blending;
(b) an additional hour of purification;
(c) an additional hour of labor.
Write a short memo to the vice-president of production recommending whether the availability of any of the three resources (blending, purification, or labor) should be increased from current levels. If you recommend an increase, specify at most how much the company should be willing to pay for an additional hour of that resource and justify your recommendation.
A chemical manufacturing company produces three types of industrial solvents, S-1,S-2, and S-3. The profits per thousand gallons for the three solvents are $300, $500, and $800 respectively. The production process requires blending and purification. It also requires additional labor for handling the finished products. The company has 260 hours of blending, 300 hours of purification, and 160 labor hours available. The requirements for each solvent are shown in the table below:
S-1 S-2 S-3
Blending (hours/1000gallons)
2 2 3
Purification (hours/1000gallons)
1 2 4
Labor (hours/1000gallons)
1 2 2
1. Formulate a linear program that can be used to determine the optimal product mix for the chemical company. Specifically, do the following: Identify the decision variables (make sure that you specify the units for these variables). Specify the objective function and the relevant constraints.
2. The production manager uses a DSS to obtain the optimal production mix. For this optimal product mix, 250 hours of blending, 300 hours of purification, and 160 hours of labor are required. The maximum attainable profit is desired. Develop a simple DSS prototype to solve this production planning problem and to confirm the optimal solutions.
a. How many gallons of S-1, S-2, and S-3 are produced under this optimal product mix?
b. What is the maximum attainable profit?
c. What is the profit contribution for each solvent (S-1, S-2, S-3)?
3. Perform sensitivity analysis to determine how much should the manager be willing to pay for:
(a) an additional hour of blending;
(b) an additional hour of purification;
(c) an additional hour of labor.
Write a short memo to the vice-president of production recommending whether the availability of any of the three resources (blending, purification, or labor) should be increased from current levels. If you recommend an increase, specify at most how much the company should be willing to pay for an additional hour of that resource and justify your recommendation.
Related questions
The Walton Toy Company manufactures a line of dolls and a doll dress sewing kit. Demand for the dolls is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) | Selling Price per Unit | Direct Materials | Direct Labor |
| Debbie | 66,000 | $37.00 | $4.30 | $3.50 |
| Trish | 58,000 | $ 5.00 | $1.20 | $0.84 |
| Sarah | 51,000 | $35.50 | $8.84 | $5.60 |
| Mike | 37,000 | $15.00 | $3.60 | $4.20 |
| Sewing kit | 341,000 | $ 9.60 | $4.80 | $0.49 |
| The following additional information is available: |
| a. | The companyâs plant has a capacity of 115,730 direct labor-hours per year on a single-shift basis. The companyâs present employees and equipment can produce all five products. |
| b. | The direct labor rate of $7 per hour is expected to remain unchanged during the coming year. |
| c. | Fixed costs total $545,000 per year. Variable overhead costs are $3 per direct labor-hour. |
| d. | All of the company's nonmanufacturing costs are fixed. |
| e. | The companyâs finished goods inventory is negligible and can be ignored. |
| Required: | ||||||||||||
| 1. | Determine the contribution margin per direct labor-hour expended on each product. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
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| 2. | Calculate the the total direct labor-hours that will be required to produce the units estimated to be sold during the coming year. (Do not round intermediate calculations.)
|
| 3. | Based on response to Requirement 1 & 2, how much of 115,730 direct labor hours of capacity will be allocated to Walton Toy Companyâs various products?
|
| 4. | What is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? Total margin contribution:
highest price per hour: |
