Concept explainers
a)
To determine: The way the company can maximize the profit.
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 use: A solver table to analyze the effect on profit of changing the minimum percentage of nitrogen required in fertilizer 1.
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.
c)
To use: A solver table to analyze the effect of the change on the profit.
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, Loose-leaf Version
- You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.arrow_forwardIn the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?arrow_forwardSix months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of 150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of 250 per room. a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100. b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?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_forwardA 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_forwardA firm sells two products. Product R sells for $20; its variable cost is $6. Product S sells for $50; its variable cost is $30. Product R accounts for 60 percent of the firm’s sales, while S accounts for 40 percent. The firm’s fixed costs are $4 million annually. Calculate the firm’s break-even pointarrow_forward
- Giapetto is thinking of buying a new cutting tool for $25 to make toy soldiers and a new clamping tool for $20 to make toy trains. If he does not buy a new tool, he can still make a toy using the older tool he already has. However, using an old cutting tool leads to 50% of the produced soldiers and using an old clamping tool leads to 40% of the produced trains to be defective. With a new tool, there is no defective production. Giapetto cannot sell any defective product. Weekly demands (must be met exactly without left-over inventory) and productions costs are as follows: 1. Soldiers 2. Trains Demand (units/week) Production cost (S/unit) 100 300 12 14 There are other details about the problem which will be added later. Giapetto started formulating a mathematical model considering only the above description and defined the following decision variables: yi: Production quantity for type i toy, i = 1, 2 corresponding to soldiers and trains, respectively. Considering the above problem…arrow_forwardMartin owns an older home, which requires minor renovations. However, the neighborhood where Martin lives mostly includes newly constructed luxury homes. Why might Martin's home increase in value? Based on the principle of substitution, the value of Martin's house will equal the value of the newly constructed homes in the neighborhood. ○ The value of Martin's home will decrease due to the new competition in the neighborhood. Based on the principle of regression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood. Based on the principle of progression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood.arrow_forwardLong-Life Insurance has developed a linear model that it uses to determine the amount of term life Insurance a family of four should have, based on the current age of the head of the household. The equation is: y=150 -0.10x where y= Insurance needed ($000) x = Current age of head of household b. Use the equation to determine the amount of term life Insurance to recommend for a family of four of the head of the household is 40 years old. (Round your answer to 2 decimal places.) Amount of term life insurance thousandsarrow_forward
- Assume the demand for a company's 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. a. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years. Consider a capacity range from 40,000 to 80,000, at 5,000 unit increments. 80,000 b. Determine how large a Wozac plant the company should build to maximize its NPV over the next 10 years. Consider a capacity range from 40,000 to 80,000, at 5,000 unit increments, and assume a 10% discount rate. 40,000arrow_forwardConsider the simple von-Thunen model of agricultural land use developed in class. This question asks you to analyze the land use of carrot farmers who use a fixed proportion production technology. Assume the following: -- carrot yield (E) is 20 tons per acre -- carrots sell at $15 per ton (P) at the market -- non-land input costs (I) are $60 per acre -- transport cost (t) is $4 per ton per mile -- farmers pay the transport cost of moving carrots d miles to the market a. Derive the bid-rent curve per acre of land for carrot farmers by imposing the appropriate long-run equilibrium condition. Explain the condition. Show all steps. b. Plot the bid-rent curve for carrot farmers. Then calculate the land area where carrots are grown. c. How much will the landlord charge to rent 1 acre at the city? at d=1 mile? at d = 5 miles? Show computations. d. Where does Farmer Jones prefer to locate? Whyarrow_forwardFRUIT COMPUTER COMPANY Fruit Computer Company manufactures memory chips in batches of ten chips. From past experience, Fruit knows that 80% of all batches contain 10% (1 out of 10) defective chips, and 20% of all batches contain 50% (5 out of 10) defective chips. If a good (that is, 10% defective) batch of chips is sent to the next stage of production, processing costs of $4000 are incurred, and if a bad batch (50% defective) is sent on to the next stage of production, processing costs of $16000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $4000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $400, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. QUESTIONS 1.Determine a strategy so Fruit can minimize the expected total cost per batch. 2.Compute the EVSI and EVPI.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,