31 May Question 9. A furniture store has set aside 800 square feet to display its
Question
9. A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
| a. | Write a mathematical model representing the store’s constraints. | |
| b. | Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model each of the following objectives: | |
| 1. | Maximize the total pieces of furniture displayed. | |
| 2. | Maximize the total expected number of daily sales. | |
| 3. | Maximize the total expected daily profit. |
10. A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time. Work area #2 has 48 hours of available production time. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and $6 per window.
| a. | Define decision variables that will tell how many units to build (doors and windows). |
| b. | Develop an objective function that will maximize profits. |
| c. | Develop production constraints for work area #1 and #2. |
11. A small firm builds television antennas. The investment in plan and equipment is $200,000. The variable cost per television antenna is $500. The price of the television antenna is $1000. How many television antennas would be needed for the firm to break even?
12. As computer service center has the capacity to do 400 jobs per day. The expected level of jobs demanded per day is 250 per day. The fixed cost of renting the computer process is $200 per day. Space rents for $100 per day. The cost of material is $15 per unit of work and $.35 cents of labor per unit. What is the break-even level of work?
13. To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs are estimated as follows. Annual fixed costs to operate the school are $30,000. The annual cost per car is $3000. The cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is $350. Let x be the number of cars and y be the number of students.
| a. | Write an expression for total cost. |
| b. | Write an expression for total revenue. |
| c. | Write an expression for total profit. |
| d. | The school offers the course eight times each year. Each time the course is offered, there are two sessions. If they decide to operate five cars, and if four students can be assigned to each car, will they break even? |
14. Zipco Printing operates a shop that has five printing machines. The machines differ in their capacities to perform various printing operations due to differences in the machines’ designs and operator skill levels. At the start of the workday there are five printing jobs to schedule. The manager must decide what the job-machine assignments should be.
| a. | How could a quantitative approach to decision making be used to solve this problem? |
| b. | What would be the uncontrollable inputs for which data must be collected? |
| c. | Define the decision variables, objective function, and constraints to appear in the mathematical model. |
| d. | Is the model deterministic or stochastic? |
| e. | Suggest some simplifying assumptions for this problem. |
15. Consider a department store that must make weekly shipments of a certain product from two different warehouses to four different stores.
| a. | How could a quantitative approach to decision making be used to solve this problem? |
| b. | What would be the uncontrollable inputs for which data must be gathered? |
| c. | What would be the decision variables of the mathematical model? the objective function? the constraints? |
| d. | Is the model deterministic or stochastic? |
| e. | Suggest assumptions that could be made to simplify the model. |
16. Three production processes – A, B, and C – have the following cost structure:
| Process | Fixed Cost
per Year |
Variable Cost
per Unit |
| A | $120,000 | $3.00 |
| B | 90,000 | 4.00 |
| C | 80,000 | 4.50 |
a. What is the most economical process for a volume of 8,000 units?
b. How many units per year must be sold with each process to have annual profits of $50,000 if the selling price is $6.95 per unit?
c. What is the break-even volume for each process?
17. Jane Persico, facility engineer at the El Paso plant of Computer Products Corporation (CPC), is studying a process selection decision at the plant. A new printer is to be manufactured and she must decide whether the printer will be auto-assembled or manually assembled. The decision is complicated by the fact that annual production volume is expected to increase by almost 50% over three years. Jane has developed these estimates for two alternatives for the printer assembly process:
| Auto-
Assembly Process |
Manual |
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