What is total cost of manufacturing and purchasing plan

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Reference no: EM132478498

Linear Programming: Applications in Marketing, Finance, and Marketing Management

Question 1: (Algorithmic)

Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phones. Epsilon employs call center personnel to handle these reservations and to deal with website reservation system Questions and for the rebooking of flights for customers whose plans have changed or whose travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call center employees needed by day of the week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

Day	Minimum Number of Employees Needed
Monday	45
Tuesday	90
Wednesday	60
Thursday	75
Friday	50
Saturday	45
Sunday	60

The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on any day of the week. Each call center employee receives the same salary. Assume that the schedule cycles and ignore start up and stopping of the schedule.

Develop a model that will minimize the total number of call center employees needed to meet the minimum requirements.

Let Xi = the number of call center employees who start work on day i
(i = 1 = Monday, i = 2 = Tuesday...)

Min	X₁ +	X₂ +	X₃ +	X₄ +	X₅ +	X₆ +	X₇
s.t.
	X₁ +			X₄+	X₅+	X₆+	X₇	≤ ≥ =
	X₁ +	X₂+			X₅+	X₆+	X₇	≤ ≥ =
	X₁ +	X₂+	X₃+			X₆+	X₇	≤ ≥ =
	X₁ +	X₂+	X₃+	X₄+			X₇	≤ ≥ =
	X₁ +	X₂+	X₃+	X₄+	X₅			≤ ≥ =
		X₂ +	X₃+	X₄+	X₅+	X₆		≤ ≥ =
			X₃ +	X₄+	X₅+	X₆+	X₇	≤ ≥ =
	X₁,	X₂,	X₃,	X₄,	X₅,	X₆,	X₇	≥	0

Find the optimal solution.

X₁	=
X₂	=
X₃	=
X₄	=
X₅	=
X₆	=
X₇	=

Total Number of Employees =

Give the number of call center employees that exceed the minimum required.

Excess employees:

Monday =

Tuesday =

Wednesday =

Thursday =

Friday =

Saturday =

Sunday =

Question 2:

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.46 per pound for Brazilian Natural and $0.64 per pound for Colombian Mild. The compositions of each coffee blend are as follows:

	Blend
Bean	Regular	DeCaf
Brazilian Natural	60%	40%
Colombian Mild	40%	60%

Romans sells the Regular blend for $3.1 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 1050 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.8 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.15 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit.
Let BR = pounds of Brazilian beans purchased to produce Regular
BD = pounds of Brazilian beans purchased to produce DeCaf
CR = pounds of Colombian beans purchased to produce Regular
CD = pounds of Colombian beans purchased to produce DeCaf

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

The complete linear program is (attached)

What is the contribution to profit?

Optimal solution:
BR =

BD =

CR =

CD =

If required, round your answer to two decimal places.

Value of the optimal solution = $

Question 3:

As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars):

Year	1	2	3	4	5	6
Payment	180	220	245	300	320	480

The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings (at 3.75% annually) and government securities, at prices and rates currently quoted in The Wall Street Journal.

Hoxworth wants to develop a plan for making the annual payments by investing in the following securities (par value = $1000). Funds not invested in these securities will be placed in savings.

Security	Current Price	Rate (%)	Years to Maturity
1	$1065	6.25	3
2	$1000	5.225	4

Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan.

b. Use linear programming to find the minimum cash settlement necessary to fund the annual payments.
Let
F = total funds required to meet the six years of payments
G1 = units of government security 1
G2 = units of government security 2
Si = investment in savings at the beginning of year i
c.
Note: All decision variables are expressed in thousands of dollars.

If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

d. Round your answer to the nearest dollar. If an amount is zero, enter "0".

Current investment required $

Investment in government security 1 $

Investment in government security 2 $

Investment in savings for year 1 $

Investment in savings for year 2 $

Investment in savings for year 3 $

Investment in savings for year 4 $

Investment in savings for year 5 $

Investment in savings for year 6 $

f. Use the dual value to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000. Round your answer to the nearest dollar.

g. Use the dual value to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000. Round your answer to the nearest dollar.

Hoxworth should be willing to pay anything less than $ .

h. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change.

Note: All decision variables are expressed in thousands of dollars.

If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

i. How much would Hoxworth save if this change could be negotiated? Round your answer to the nearest dollar.

1. Question 9-17

Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows:

a. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased? If required, round your answers to one decimal place.
Let FM = number of frames manufactured
FP = number of frames purchased
SM = number of supports manufactured
SP = number of supports purchased
TM = number of straps manufactured
TP = number of straps purchased
b.

c.
FM, FP, SM, SP, TM, TP ≥ 0.

d. Manufacture Purchase
Frames

Supports

Straps

f. What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar.

$
g. How many hours of production time are used in each department?

i. How much should Frandec be willing to pay for an additional hour of time in the shaping department?

j. Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity?

• Yes
• No

Why or why not?

Attachment:- linear programming applications.rar

Reference no: EM132478498

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