An Electrical Utility Startup ProblemA problem faced by an electrical utility company each day is that of deciding which generators to start up.The utility in question has five generators with the characteristics shown in the following table. If anyMegawatt-hours (MW-hr) are produced by a generator, the generator must be started up and the fixedstartup cost is incurred. At least 8600 MW-hrs must be generated today. Set up and solve a linearspreadsheet model (with some binary variables) to determine the operating plan that will minimize theiroverall costs. For full credit, the model must be linear (no multiplication of changing cells, no IFstatements, no MAX statements, etc.).Fixed Startup CostCost per MW-hr GeneratedMaximum Capacity (MW-hr)GeneratorA$2400$102100GeneratorB$2800$92400Generator GeneratorCD$4000$3350$8$1027003100GeneratorE$1700$113700

Let us consider the variables A, B, C,D & E represent the Generators A,B,C,D & E. Now, let…

Answered: An Electrical Utility Startup Problem A…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P

See similar textbooks

Similar questions

Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?
Formulate and then solve a linear programming model of this problem, to determine how manycontainers of each product to produce tomorrow to maximize profits. The company makes fourjuice products using orange, grapefruit, and pineapple juice.Product Retail Price per QuartOrange juice $1.00Grapefruit juice .90Pineapple juice .80All-in-One 1.10The All-in-One juice has equal parts of orange, grapefruit, and pineapple juice. Each product isproduced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orangejuice, 300 gallons of grapefruit juice, and 200 gallons of pineapple juice. The cost per gallon is$2.00 for orange juice, $1.60 for grapefruit juice, and $1.40 for pineapple juice.In addition, the manager wants grapefruit juice to be used for no more than 30 percent of thenumber of containers produced. She wants the ratio of the number of containers of orange juice tothe number of containers of pineapple juice to be at least 7 to 5.
A call center employs 1,425 agents. Every month 57 employees leave the company and 57 new employees are hired. a. How long on average does an agent work for this call center (in months) Suppose the cost of hiring and training a new agent is $1,140. The manager of this call center believes that increasing agents’ salaries would keep them working longer at the company. The manager wants to increase the average time that an agent works for the call center to 36 months, or three years. b-1. Given the current average working time for agents at this call center, determine the current annual cost for hiring and training. b-2. Assuming the average time that an agent works for the call center is increased to 36 months, determine the new annual cost for hiring and training. b-3. If the time an agent works for the call center is increased to 36 months on average, how much could the company save on hiring and training costs over a year?
A company manufactures two types of trucks. Eachtruck must go through the painting shop and the assembly shop. If the painting shop were com-pletely devoted to painting type 1 trucks, 650 per day could be painted, whereas if the painting shopwere completely devoted to painting type 2 trucks,550 per day could be painted. If the assembly shopwere completely devoted to assembling truck 1engines, 1400 per day could be assembled, whereasif the assembly shop were completely devoted toassembling truck 2 engines, 1000 per day could beassembled. It is possible, however, to paint bothtypes of trucks in the painting shop. Similarly, it ispossible to assemble both types in the assemblyshop. Each type 1 truck contributes $2500 to profit; each type 2 truck contributes $3000. Use Solver to maximize the company’s profit. (Hint: One ap-proach, but not the only approach, is to try a graphi-cal procedure first and then deduce the constraints from the graph.)
Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run theday shift and $6000 to run the night shift. Demand for the next two days is as follows: day 1, 4000; night 1, 3000; day 2, 2000; night 2, 5000. It costs $1 per unit to hold a unit in inventory for a shift.a. Determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. (Note: Not all shifts have to be run.)b. After listening to a seminar on the virtues of the Japanese theory of production, Murray has cut the setup cost of its day shift to $1000 per shift and the setup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. Show that the decrease in setup costs has actually raised the average inventorylevel. Is this…
A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40units. Each quarter, up to 27 units can be produced withregular-time labor, at a cost of $40 per unit. During eachquarter, an unlimited number of units can be produced withovertime labor, at a cost of $60 per unit. Of all unitsproduced, 20% are unsuitable and cannot be used to meetdemand. Also, at the end of each quarter, 10% of all unitson hand spoil and cannot be used to meet any futuredemands. After each quarter’s demand is satisfied andspoilage is accounted for, a cost of $15 per unit is assessedagainst the quarter’s ending inventory. Formulate an LP thatcan be used to minimize the total cost of meeting the nextthree quarters’ demands. Assume that 20 usable units areavailable at the beginning of quarter 1.
A public hospital employs volunteers to attend the reception between 8:00 A.M. and 10:00 P.M. Each volunteer works three consecutive hours, except those who enter at 8:00 P.M., who only work 2 hours. An approximation to the minimum need for volunteers is through a staggered function in two-hour intervals, which start at 8:00 A.M. and they are 4, 6, 8, 6, 4, 6 and 8 volunteers per interval. As most of the volunteers are pensioners, they are willing to offer their services at any time of the day (8:00 A.M. to 10:00 P.M.). However, as most charities compete for your services, the amount required should be kept as low as possible. Determine an optimal schedule of start time and number of volunteers.

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS