EMGT 501

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EMGT 501 HW 1 Chapter 2 - SELF TEST 18 Chapter
2 - SELF TEST 20 Chapter 3 - SELF TEST
28 Chapter 4 - SELF TEST 3 Chapter 5 - SELF
TEST 6 Due Day Sep 13
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Ch. 2 18 For the linear program

• Write this linear program in standard form.
• Find the optimal solution using the graphical
  solution procedure.
• What are the values of the three slack variables
  at the optimal solution?

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Ch. 2 20 Embassy Motorcycle (EM) manufactures
two lightweight motorcycles designed for easy
handling and safety. The EZ-Rider model has a new
engine and a low profile that make it easy to
balance. The Lady-Sport model is slightly larger,
uses a more traditional engine, and is
specifically designed to appeal to women riders.
Embassy produces the engines for both models at
its Des Moines, Iowa, plant. Each EZ-Rider engine
requires 6 hours of manufacturing time and each
Lady-Sport engine requires 3 hours of
manufacturing time. The Des Moines plant has 2100
hours of engine manufacturing time available for
the next production period. Embassys motorcycle
frame supplier can supply as many EZ-Rider frames
as needed.
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However, the Lady-Sport frame is more complex and
the supplier can provide only up to 280
Lady-Sport frames for the next production period.
Final assembly and testing requires 2 hours for
each EZ-Rider model and 2.5 hours for each
Lady-Sport model. A maximum of 1000 hours of
assembly and testing time are available for the
next production period. The companys accounting
department projects a profit contribution of
2400 for each EZ-Rider produced and 1800 for
each Lady-Sport produced.
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• Formulate a linear programming model that can be
  used to determine the number of units of each
  model that should be produced in order to
  maximize the total contribution to profit.
• Find the optimal solution using the graphical
  solution procedure.
• Which constraints are binding.

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Ch. 3 28 National Insurance Associates carries
an investment portfolio of stocks, bonds, and
other investment alternatives. Currently 200,000
of funds are available and must be considered for
new investment opportunities. The four stock
options National is considering and the relevant
financial data are as follows
Stock A B C D Price per
share 100 50 80 40 Annual rate of
return 0.12 0.08 0.06 0.10 Risk measure per
dollar invested 0.10 0.07 0.05 0.08 The risk
measure indicates the relative uncertainty
associated with the stock in terms of its
realizing the projected annual return higher
values indicate greater risk. The risk measures
are provided by the firms top financial advisor.
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• Nationals top management has stipulated the
  following investment guidelines the annual rate
  of return for the portfolio must be at least 9
  and no one stock can account for more than 50 of
  the total dollar investment.
• Use linear programming to develop an investment
  portfolio that minimizes risk.
• If the firm ignores risk and uses a maximum
  return-on-investment strategy, what is the
  investment portfolio?
• What is the dollar difference between the
  portfolios in parts (a) and (b)? Why might the
  company prefer the solution developed in part
  (a)?

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Ch. 4 3 The employee credit union at State
University is planning the allocation of funds
for the coming year. The credit union makes four
types of loans to its members. In addition, the
credit union invests in risk-free securities to
stabilize income. The various revenue-producing
investments together with annual rates of return
are as follows Type of Loan/Investment
Annual Rate of Return () Automobile loans
8 Furniture loans 10 Other secured
loans 11 Signature loans 12 Risk-free
securities 9
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• The credit union will have 2,000,000 available
  for investment during the coming year. State laws
  and credit union policies impose the following
  restrictions on the composition of the loans and
  investments.
• Risk-free securities may not exceed 30 of the
  total funds
• available for investment.
• Signature loans may not exceed 10 of the funds
  invested
• in all loans (automobile, furniture, other
  secured, and
• signature loans).
• Furniture loans plus other secured loans may not
  exceed
• the automobile loans
• Other secured loans plus signature loans may not
  exceed
• the funds invested in risk-free securities.

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How should the 2,000,000 be allocated to each of
the loan/investment alternatives to maximize
total annual return? What is the projected total
annual return?
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Ch. 5 6
40 30 15
Basis
5 2 0 3
20 1 2 0
25 0 1 -1/2
0 1 0 0
0 0 1 0
0 0 0 1

• Complete the initial tableau.
• Write the problem in tableau form.
• What is the initial basis? Does this basis
  correspond to the origin? Explain.
• What is the value of the objective function at
  this initial solution?

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• e. For the next iteration, which variable should
  enter the
• basis, and which variable should leave the
  basis?
• f. How many units of the entering variable will
  be in the
• next solution? Before making this first
  iteration, what do
• you think will be the value of the objective
  function after
• the first iteration?
• g. Find the optimal solution using the simplex
  method.

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EMGT 501 HW 1 Solutions Chapter 2 - SELF TEST
18 Chapter 2 - SELF TEST 20 Chapter 3 - SELF
TEST 28 Chapter 4 - SELF TEST 3 Chapter 5 -
SELF TEST 6
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Ch. 2 18 (a)
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Ch. 2 18 (b)
(c) s1 0, s2 0, s3 4/7
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Ch. 2 20 (a)
Let E number of units of the EZ-Rider
produced L number of units of the
Lady-Sport produced
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Ch. 2 20 (b)
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Ch. 2 20 (c)
The binding constraints are the manufacturing
time and the assembly and testing time.
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Ch. 3 28 (a)
Let A number of shares of stock A B number
of shares of stock B C number of shares of
stock C D number of shares of stock D To get
data on a per share basis multiply price by rate
of return or risk measure value.
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Solution A 333.3, B 0, C 833.3, D
2500 Risk 14,666.7 Return 18,000 (9) from
constraint 2
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Ch. 3 28 (b)
Solution A 1000, B 0, C 0, D
2500 Risk 10A 3.5B 4C 3.2D
18,000 Return 22,000 (11)
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Ch. 3 28 (c)
The return in part (b) is 4,000 or 2 greater,
but the risk index has increased by
3,333. Obtaining a reasonable return with a
lower risk is a preferred strategy in many
financial firms. The more speculative, higher
return investments are not always preferred
because of their associated higher risk.
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Ch. 4 3
x1 automobile loans x2 furniture loans x3
other secured loans x4 signature loans x5
"risk free" securities
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Solution
Annual Return 188,800 (9.44)
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Ch. 5 6 (a)
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Ch. 5 6 (b)
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Ch. 5 6 (c)
The original basis consists of s1, s2, and s3.
It is the origin since the nonbasic variables
are x1, x2, and x3 and are all zero.
(d) 0
x3 enters because it has the largest negative zj
- cj and s2 will leave because row 2 has the
only positive coefficient.
(e)
(f)
30 objective function value is 30 times 25 or
750.
(g)
Optimal Solution x1 10 s1 20 x2
0 s2 0 x3 30 s3 0 z
800.