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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;Assembly;Process;Annual fixed cost;$690,000;$269,000;Variable cost per product;$29.56;$31.69;Estimated annual production;(in number of products);Year 1;152,000;152,000;Year 2;190,000;190,000;Year 3;225,000;225,000;a.;Which production process would be the least-cost alternative in Years 1;2, and 3?;b.;How much would the variable cost per unit have to be in Year 2 for the;auto-assembly process to justify the additional annual fixed cost for the;auto-assembly process over the manual assembly process?

Paper#57865 | Written in 18-Jul-2015

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