Concept explainers
a)
To determine: The way to satisfy the mileage and demand requirement at the minimum possible cost.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
b)
To determine: The sensitivity to total cost with relation to the 23 mpg requirement and when it is greater than 27 mpg requirement.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
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Chapter 4 Solutions
Practical Management Science
- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.arrow_forwardThe Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.arrow_forwardIt costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.arrow_forward
- A young computer engineer has $12,000 to invest and three different investment options (funds) to choose from. Type 1 guaranteed investment funds offer an expected rate of return of 7%, Type 2 mixed funds (part is guaranteed capital) have an expected rate of return of 8%, while an investment on the Stock Exchange involves an expected rate of return of 12%, but without guaranteed investment capital. Computer engineer has decided not to invest more than $2,000 on the Stock Exchange in order to minimize the risk. Moreover for tax reasons, she needs to invest at least three times more in guaranteed investment funds than in mixed funds. Assume that at the end of the year the returns are those expected; she is trying to determine the optimum investment amounts. (a) Express this problem as a linear programming model with two decision variables.(b) Solve the problem with the graphical solution procedure and define the optimum solution.arrow_forwardRajan wanted a radio from Jacky's. It appears that Rajan is particularly interested in purchasing a Radio from the inexpensive retailer's sales manager for consumer electronics. He tells Jacky, the salesperson at the inexpensive store where he thinks he'll get the best deal, that his old radio died and he wants to listen to his favourite tunes. He wants a replacement radio as quickly as possible. In three and a half weeks, Rajan's favourite model will be 10% off.He suspects Rajan won't wait and will find another job. Jacky will earn less on the lowered price. He thinks that telling Rajan of the sale makes little sense.When Jacky tells Rajan that the radio set he wants is no longer available and won't be for another week, Rajan is enraged. Fearing losing the business, Jacky begs his sales manager, Michelle, to speed up delivery. Michelle says it's impossible and suggests Jacky tell Rajan the store can get the set in 24 hours and sell him the demo model. Michelle says the sample is new…arrow_forwardCould someone please me with these three questions? A is question 1 B Is 2 and the last one is split but is only one question which is 3arrow_forward
- A company owns a 5-year-old turret lathe that has a book value of $23,000. The present market value for the lathe is $18,000. The expected decline in market value is $1,700/year to a minimum market value of $4,080; maintenance plus operating costs for the lathe equal $4,470/year.A new turret lathe can be purchased for $46,000 and will have an expected life of 8 years. The market value for the turret lathe is expected to equal $46,000(0.70)k at the end of year k. Annual maintenance and operating cost is expected to equal $1,900. Based on a 12% MARR, should the old lathe be replaced now? Use an equivalent uniform annual cost comparison, a planning horizon of 7 years, and the cash flow approach.EUAC for keeping old turret lathe: $EUAC for replacing turret lathe: $arrow_forwardThe Fly-Right Airplane Company builds small jet airplanes to sell to corporations for use by their executives. To meet the needs of these executives, the company's customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers with short deadlines. However, because the company's production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the next table. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once production is under way. the marginal net revenue (which is the purchase price minus the…arrow_forwardWilliams Auto has a machine that installs tires. The machine is now in need of repair. The machineoriginally cost $10,000 and the repair will cost $1,000, but the machine will then last two years.The labor cost of operating the machine is $0.50 per tire. Instead of repairing the old machine,Williams could buy a new machine at a cost of $5,000 that would also last two years; the labor costwould then be reduced to $0.25 per tire. Should Williams repair or replace the machine if it expectsto install 10,000 tires in the next two years?arrow_forward
- Bruin Properties is in escrow to buy a 175,000 square foot shopping center in Camarillo, California for $35,000,000. Bruin Properties can borrow $24,000,000 fixed rate fully amortizing over 30 years at a 6.0% annual interest rate with equal monthly payments of principal and interest or it can borrow $28,000,000 fixed rate fully amortizing over 30 years at a 7.0% annual interest rate with equal monthly payments of principal and interest. What is the incremental annual borrowing cost for the additional $4,000,000 loan amount if each loan would be outstanding for the full 30 year term? a.13.0% b.12.4% c.11.5% d. 7.0%arrow_forwardYoda just got a job offer. The job is located in Awayville. Awayville is 70 miles north of Binghamton. Yoda wants to accept the job offer, still live in Binghamton, and commute to Awayville on a daily basis. This will result in travel expense relates to approximately 700 miles per week. To make this plan work, Yoda needs a car that will get at least 25 miles per gallon of gasoline. Yoda goes to Darth's Used Car Dealership. Yoda tells Darth that Yoda needs a car that gets at least 25 miles per gallon of gasoline. Yoda explains the Awayville job situation and Darth says, "I understand - I will check my inventory - I will be right back." Darth goes into his office and looks through two different files of used car inventory. One file contains all cars that get over 25 miles per gallon of gasoline and the other file contains all cars that get under 25 miles per gallon of gasoline. Darth selects a used car from the file that indicates that the cars get over 25 miles per gallon of gasoline…arrow_forwardA retail store sold in the month of April 5,000 products that produced $45,000 in sales. In the month of May the company sold 6,000 products. The store workforce consists of four full-time workers who work 40-hour week. In April the store also had seven part-time workers at 10 hours per week, and in May the store had nine part-timers at 15 hours per week (assume four weeks in each month). Using sales dollars as the measure of output (assume the price of the product was the same for both months), what is the percentage change in labor productivity from April to May? Answer: 2.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,