Classwork for LP and Graphing_Nov 1
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Florida Agricultural and Mechanical University *
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3602
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Industrial Engineering
Date
Dec 6, 2023
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Class Exercise for Linear Programming and Graphing (November 1, 2023)
1.
Consider the linear program below. Graph the constraints, identify the feasible region, show the
vertices for the feasible region, and identify the optimal corner point (Optimal Solution).
Next, draw the objective function line using Z=35
Max Z = 5X
1
+7X
2
Subject to:
X
1
≥ 2
2X
1 +
4X
2
≤ 24
X
1 +
4X
2
≤ 8
X
1
,
X
2
≥ 0
2.
Josephine Investments manages funds for a number of companies and wealthy clients. The
investment strategy is tailored to each client's needs. For a new client, Josephine has been
authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market
fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each
unit of the money market fund costs $100 and provides an annual rate of return of 4%.
The client
wants to minimize risk subject to the requirements that the annual income from investment
be at least $60,000
. According to Josephine’s risk measurement system, each unit invested in the
stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index
of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier
investment. Josephine’s client also specified that at least $300,000 be invested in the money
market fund.
Develop a linear programming model.
3.
As part of a quality improvement initiative, Cotton Electronics employees complete a three-day
training program on teaming and a two-day training program on problem-solving. The manager
of quality improvement has requested that at least 8 training programs on teaming and at least 10
training programs on problem-solving be offered during the next six months. In addition, senior-
level management has specified that at least 25 training programs must be offered during this
period. Cotton Electronics uses a consultant to teach the training programs. During the next
quarter, the consultant has 84 days of training time available. Each training program on teaming
costs $10,000 and each training program on problem-solving costs $8000.
Formulate a linear programming model
that can be used to determine the number of training
programs on teaming and the number of training programs on problem-solving that should be
offered in order to minimize total cost.
Class Exercise for Linear Programming and Graphing (November 1, 2023)
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