Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 4, Problem 123P
Summary Introduction
To determine: The way Company C can maximize the revenue.
Linear programming:
It is a mathematical modeling procedure were 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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Larry’s Bakery operates a chain of ten high-end bakeries. Larry, the owner of these amazing bakeries, is looking at two options to increase his revenues throughout his chain of bakeries.
The first option is to launch a loyalty card. Doing this would cost Larry $500,000. The probability that this would result in high sales is 0.6, which means the probability it would result in low sales is 0.4. If high sales are generated from this option, Larry can expect to see additional revenues of $1,000,000. If low sales are generated from this option, Larry can expect to see additional revenues of only $750,000.
The second option Larry has is to cut the prices throughout his bakeries. Doing so would cost him $300,000. The probability that this would result in high sales is 0.8. If doing this results in high sales, Larry can expect to see additional revenues of $800,000. If it results in low sales, he can expect to see additional revenues of only $500,000.
Larry obviously has a tough decision…
Stock in Company A sells for $89 a share and has a 3-year average annual return of $24 a share. The beta value is 1.26. Stock in Company B sells for $83 a share and has a 3-year average annual return of $18 a share. The beta value is 1.13.
Derek wants to spend no more than $19,000 investing in these two stocks, but he wants to earn at least $2100 in annual revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy.
Set up the linear programming problem. Let a represent the number of shares of stock in Company A, b represent the number of shares of stock in Company B, and z represent the total beta value.
Minimize
z3 1.26а + 1.13b
subject to
89а + 83b s
19000
24a + 18b >
2100
a 2 0, b20.
(Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.)
Derek should buy 88 share(s) of stock in Company A and 0 share(s) of stock in Company B.
(Round to the nearest integer as needed.)
Long-Life Insurance developed a linear model to determine the amount of term life insurance a family of four should have, based on the head of the household's current age.
The equation is: y = 163 -0.45xwherey = Insurance needed ($000)x = Current age of head of household
Calculate the amount of term life insurance you would recommend for a family of four if the head of the household is 53 years old. (Round your answer to 2 decimal places.)
Chapter 4 Solutions
Practical Management Science
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