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# MD235 Fall 2011 Exam 3 VanderWerf Solutions.pdf

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Boston College

Business Law

BSLW 1102

Pieter Vander Werf

Fall

Description

Boston College
MD235, Sections 3 and 4
Fall 2011
Exam 3
Print your name___________________________________
Sign the cover page and initial each later page in the upper-right on the line provided. There are 5
questions, most with several parts. The points for each part are given in parentheses. Do all work on the
test paper. Show your work or explain your reasoning on questions whose instructions call for it.
There should be enough room on the front. Use the spaces provided to report your answers.
(Chap. 7)
1. Healy Sportswear Corporation is considering options for investing its capital budget. They are:
A. Developing a new line of women’s tops.
B. Releasing the cross-training shoe developed last year.
C. Executing a buyback of the company’s stock.
D. Buying competitor Doyle Corporation.
E. Opening 1-3 new factories.
F. Expanding sales into one or more West Coast cities, up to ten.
Healy has ordered you to formulate a linear program to decide which of these investments to make. In
these decisions no fractions are allo wed (You can’t develop just some of the tops, buy back only some
of the stock, buy a fraction of Doyle, open 1.5 factories, expand into 1.8 cities, etc.)
1a. (7 points) Create a decision variable for each of these investment decisions. In the table below, list a
symbol for each one, define it, and list any required constraints on its possible values:
Decision
Variable Constraints on the value of
Investment Symbol Definition the decision variable
A XA =1 if Healy develops the new line of tops,X As binary
otherwise
B XB =1 if Healy releases the shoe, 0 otherwiseX Bs binary
C XC =1 if Healy buys back the stock, 0 otherwiX Cs binary
=1 if Healy buys Doyle, 0 otherwise
D XD X Ds binary
E XE the number of factories Healy opens X Es integer
X E= 0
F XF The number of West Coast cities Healy expaX Fs integer
into
X F= 0
Page 1 of 9 Initials: ____________
FOR EACH OF THE QUESTIONS 1b THROUGH 1f BELO W, write one constrai nt that insures the
linear program follows the restriction(s) listed in the question, without adding any restrictions not listed
in the question.
1b. (2 points) Healy does not want to develop the line of tops if it does not release the new shoe.
X A= X B
1c. (2 points) Healy does not want to buy Doyle if it executes the stock buyback.
X D= ( 1 – X C
1d. (3 points) Healy does not want to open any new factories if it executes its stock buyback.
X E= 3(1-X )C
(If you don’t multiply by 3, then this accidentally limits you to 1 factory.)
1e. (3 points) Healy only wants to release the shoe if it develops the tops and does not buy Doyle.
2X B<= X +A(1 – X )D
Or
X B= X * A1 – X ) D
1f. (3 points) Healy wants to open at least one new factory if it expands to 1-5 West Coast cities, and at
least 2 new factories if it expands to 6-10 new cities.
X E>= X /F
Page 2 of 9 Initials: ____________
(Chap. 7)
2. Thresher Investments must invest all $100,000 of a client’s money, but in doing so it must:
Maximize the total return. (It knows the projected rate of return for each investment.)
Invest only in three different investments: Stock 1, Stock 2, and the money market.
Invest only in round lots of 100 shares for the stocks. (In the money market it can invest any
number of dollars or fractions of a dollar.)
Not invest more than $70,000 in either Stock 1 or Stock 2.
Thresher has created a linear program to decide how much to put in each investment. The spreadsheet
for the linear program is correct, but Thresher has not filled in the formulas yet. A printout of the
spreadsheet is below:
2a. (6 points) In the space below, write the Excel formula that Thresher should put in cell B11 using
Excel cell numbers and notation.
= C4*C5*C6*C8 + D4*D5*D6*D8 + E5*E8
2b. (5 points) In the space below, write the Excel formula that Thresher should put in cell B14 using
Excel cell numbers and notation.
=C4*C6*C8 + D4*D6*D8 + E8
Page 3 of 9 Initials: ____________
2c. (4 points) In the space below, write the Excel formula that Thresher should put in cell B15 using
Excel cell numbers and notation.
= C4*C6*C8
2d. (4 points) Are there any other constraints that Thresher will need to enter into Solver other than the
ones shown on lines 14 through 16? If so, describe what they are below.
Must enter that C8 and D8 are integer.
Must enter that all decision variables are > 0
Page 4 of 9 Initials: ____________
(Chap. 7)
3. Carver Corp. manufactures smart phones. The company needs to invest in additional production
capacity. There are two different types of production lines it can invest in: low-volume and high-
volume. Each of these requires a different total amount of investment, has a different production
capacity (number of cell phones it can produce each year), and has a different manufacturing cost per
unit, as follows:
Type of production line Investment required Production Manufacturing cost
($ per production linecapacity ($/unit)
(units/year) for
each line
Low-capacity 17,000,000 90,000 57
High-capacity 33,000240,0052
Carver can invest in any whole number of Low-capacity production lines and any whole number of
High-Capacity production lines. It cannot invest in a fraction of a production

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