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Please answer the following questions giving all details:
1. The Charm City Bakery makes coffee cakes and Danish pastries in large pans. The main
ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available.
The demand for coffee cakes is less than or equal to 5. Five pounds of flour and 2 pounds of
sugar are required to make a pan of coffee cakes, and 5 pounds of flour and 4 pounds of sugar are
required to make a pan of Danish pastries. A pan of coffee cakes has a profit of $6, and a pan of
Danish pastries has a profit of $5. Determine the number of pans of cakes and Danish pastries to
produce each day so that profit will be maximized.
(a) Formulate a linear programming model for this problem.
(b) Find the optimal solution of this model by hand using the corner points graphical method.
2. Solve the following linear programming model graphically. In addition, write the problem in
standard form and do a constraint analysis for the optimal solution.
Minimize 8x + 12y
Subject to
5x + 2y ≥ 40
2x + 4y < 56
x, y > 0
3. Love My Pet Foods produces dog food, made from beef products and grain. Each pound of
beef products costs $1.40, and each pound of grain costs $0.75. A pound of the dog food must
contain at least 8 units of Vitamin 1 and 10 units of Vitamin 2. A pound of beef products contains
10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of grain contains 7 units of Vitamin 1
and 8 units of Vitamin 2. How many pounds of beef and grain should be included in each pound
of dog food to minimize total cost?
(a) Define the decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
4. Determine whether the following linear programming problem is infeasible, unbounded, or has
multiple optimal solutions. Draw a graph and explain your conclusion.
Maximize Z = 15x + 20y
Subject to
-3x + 4y < 60
2x + 2y > 80
x, y ≥ 0 1 Question 5 and 7: 1 Point each
Question 6: 2 Points
5. The Charm City Food Services Company delivers fresh sandwiches each morning to vending
machines throughout the city. The company makes three kinds of sandwiches—ham and cheese,
grilled vegetables and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes,
a grilled vegetables sandwich requires 0.4 minutes, and a chicken salad sandwich requires 0.60
minutes to make. The company has 960 available minutes each night for making the sandwiches.
The profit for a ham and cheese sandwich is $0.40, the profit for a grilled vegetables sandwich is
$0.35 and the profit for a chicken salad sandwich is $0.50. The total number of sandwiches must
be less than or equal to 2000. The company can make only 500 or less of ham and cheese
sandwiches.
The company’s management wants to know how many of each kind of sandwich it should make
to maximize profit.
Formulate a linear programming model for the above situation by determining
(a) The decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Hint: There are 3 variables and 3 constraints (in addition to the non-negativity constraints) for this
problem.
6. Find the computer solution, including the sensitivity analysis (ranging) results, for Question 5
by using QM for Windows or Excel. Determine the optimal solution and optimal profit. Interpret
the optimal solution and optimal profit.
7. Answer the following questions by using the sensitivity analysis (ranging) results from
Question 6. Do NOT solve the problem again by using any computer software.
(a) If the profit from a ham and cheese sandwich increases from $0.4 to $0.5, will the optimal
number the three kinds of sandwiches made change? Will the total profit change? If they change,
what will be the new optimal solution and the new total profit?
(b) If the profit from a grilled vegetables sandwich increases from $0.35 to $0.45, will the optimal
number of the three kinds of sandwiches made change? Will the total profit change?
(c) The company has an opportunity to acquire some extra minutes of sandwich making. What is
the maximum price the company should pay for each minute of additional sandwich making time,
and how many additional minutes of sandwich making should they acquire at that price? 8. A manufacturing company produces diesel engines in four factories located in Phoenix, Seattle,
Baltimore, and Cleveland. Three trucking firms purchase these engines for their plants located in
Nashville, Orlando, and Charleston. The supplies and demands, along with the per engine
transportation costs in dollars are given below:
Plant
Nashville
Orlando
Charleston
Supply
__________________________________________________________________
Phoenix
880
1150
500
20 2 Factory Seattle
650
1050
700
30
Baltimore
550
815
472
10
Cleveland
620
910
520
25
__________________________________________________________________
Demand
35
20
25 (a) Formulate a linear programming problem to minimize total cost for this transportation
problem.
(b) Solve the linear programming formulation from part (a) by using either Excel or QM for
Windows. Find and interpret the optimal solution and optimal value. Please also include the
computer output with your submission.
The following questions are mathematical modeling questions. Please answer by defining
decision variables, objective function, and all the constraints. Write all details of the formulation.
Please do NOT solve the problems after formulating.
9. A woman wants to set up a trust fund for her two children using $1,200,000. The trust fund has
three investment options: a bond fund, a stock fund, and treasury bills fund. The projected returns
over the life of the investments are 4.2% for the bond fund, 6.2% for the stock fund, and 5% for
the treasury bills fund. She wants to invest at least 30% of the total amount in the bond fund, at
least 25% in the stock fund, and at least 20% in the treasury bills fund. She also wants the amount
invested in the treasury bills fund to be more than or equal to the amount invested in the stock
fund. She wants to know how much money should be invested in each of the three alternatives to
maximize the total projected returns.
Formulate a linear programming model for the above situation by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
10. A builder is developing a lakeside community. After considering possible advertising media
and the market to be covered, the builder has decided to advertise in four media. He collected
data on the number of potential customers reached, the cost per advertisement, the maximum
number of advertisements available, and the exposure quality rating for each of the four media.
These data are given in the following table. 3 Number of
Maximum
Potential
Number of
Exposure
Customers
Cost ($) per
Advertisements Quality
Advertising Media
Reached
Advertisement Available
Units
____________________________________________________________________________
Daytime TV (1 min ad)
2500
3500
10
75
Evening TV (30 sec ad)
4000
5200
8
80
Daily newspaper (full page ad) 1700
500
18
45
Sunday newspaper magazine 2450
1200
8
60
(1/2 page color ad)
The builder has an advertising budget of $60,000 for the campaign. In addition, he wants the
following restrictions: At least 8 television commercials must be used, at least 32,000 potential
customers must be reached, and no more than $12,000 may be spent on Sunday newspaper
magazine advertisements. What advertising media selection plan should be recommended to
maximize the total exposure quality units?
Formulate a linear programming model for the above situation by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
11. A dispatcher for a taxi company has four taxicabs at different locations and three customers
who have called for service. The mileage from each taxi’s present location to each customer is
shown in the following table:
Customer
Cab
1
2
3
__________________________
A
6
2
4
B
4
3
5
C
8
7
6
D
2
5
2
The company does not want to send cab B to customer 3 because cab B does not have the quality
customer 3 requested.
Formulate an assignment problem to minimize the total mileage for the cabs to reach the 3
customers by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating. 4

 

Please answer the following questions giving all details.
Questions 1 and 3: 1.2 Points each
Question 2: 1.6 Points
1. The Charm City recently purchased a 35 acre of farm land, and it has $500,000 budgeted to
develop recreational facilities. They are considering the facilities for soccer fields, swimming
pool, walking trails, and a children’s playground to develop. The following table shows the
amount of acreage required by each project, the annual expected usage for each facility, and the
cost to construct each facility. Also included is a priority designation determined by the town’s
recreation committee based on several public hearings and their perceptions of the critical need of
each facility.
Facility
Annual Usage (people)
Swimming pool
15,000
Soccer fields
12,000
Playground
32,000
Walking trails
30,000 Acres
6
10
14
22 Cost ($)
125,000
120,000
150,000
90,000 Priority
1
2
1
1 The total priority level cannot be more than 3. At least 2 facilities must be selected. Formulate a
capital budgeting problem that will maximize the total annual usage by determining:
(a) The decision variables.
(b) The objective function. What does it represent?
(c) All the constraints. What does each constraint represent?
Note: Do NOT solve the problem after formulating.
2. The director of career advising at the Charm City Community College wants to use decision
analysis to provide information to help students decide which 2-year degree program they should
pursue. The director has set up the following payoff table for four of the most popular and
successful degree programs at the college that shows the estimated 5-year gross income (in
thousands of dollars) from each degree for three future economic conditions:
Degree Program
Graphic design
Nursing
Real estate
Medical technology Recession
140
120
110
150 Economic Condition
Average
Good
160
160
180
200
180
220
150
150 Determine which 2-year degree program to pursue and the profit associated with it by finding the
optimal decision using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Minimax regret
3. For the problem given in Question 2, the probabilities for the economic conditions are given by
P(Recession) = 0.2, P(Average) = 0.5, and P(Good) = 0.3. a. Compute the expected value for each decision and select the best one.
b. Compute the expected regret value for each decision and select the best one.
c. Calculate and interpret the expected value of perfect information.
4. A single-server queuing system with an infinite calling population and a first-come, first-served
queue discipline has the following arrival and service rates:
λ = 70 customers per hour
µ = 100 customers per hour
Determine P1, P3, L, Lq, W, Wq, and U.
Note: Do hand calculations to answer this question.
5. An immigration agent at an airport, on an average, could process 14 entrants in one hour, if he
was busy all the time. On an average, an entrant arrives at his station at every 5 minutes. The
agent can be replaced by a more efficient specialist. The specialist can process 18 entrants in one
hour. The specialist is paid $45 per hour whereas the current agent is paid $30 per hour. If an
entrant’s time is considered to be worth $10 per hour, is it worth to replace the agent with the
specialist?
Note: Do hand calculations to answer this question.
6. A grocery store has three check-out counters. The average service rate for each check-out
counter is 25 customers per hour. The average arrival rate is 60 customers per hour. Assuming it
is a multiple-server waiting line model; determine the average number of customers waiting for a
check-out counter and the average time a customer must wait for a check-out counter. What is the
probability that there will be less than or equal to 4 customers in the system?
Note: Use QM for Windows to answer this question.

Attachments:

• 1492951039-SETof11.doc
• 1492951040-Setof6.docx