31 May Question 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. Wor
Question
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:
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