Reference no: EM132477534

Problem 1

Draw the Network Model for the following equation and related constraints:

Min	2XAX + 3XAY + 5XAZ+ 9XBX + 12XBY + 10XBZ
s.t.	XAX + XAY + XAZ≤ 500
	X BX + XBY + XBZ≤ 400
	XAX + XBX          = 300
	XAY + XBY          = 300
	XAZ + XBZ          = 300
	Xij≥ 0

Problem 2

The Grand Movie Theater has one box office clerk. On average, each customer that comes to see a movie can be sold its ticket at the rate of 6 per minute. For the theater's normal offerings of older movies, customers arrive at the rate of 3 per minute. Assume arrivals follow the Poisson distribution and service times follow the exponential distribution.

a. What is the average number of customers waiting in line?
b. What is the average time a customer spends in the waiting line?
c. What is the average number of customers in the system?
d. What is a customer's average time in the system?
e. What is the probability that someone will be buying tickets when an arrival occurs?

Problem 3

Solve the following Problem graphically.

Max X + 2Y
s.t. 6X + 8Y ≤ 48
7X + 5Y ≥ 35
X, Y ≥ 0
Y is integer

a. Graph the constraints for this Problem. Indicate all feasible solutions.
b. Find the optimal solution to the LP Relaxation. Round down to find a feasible integer solution. Is this solution optimal?
c. Find the optimal solution.

Problem 4

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:

Production Time (hours)
Model	Cutting and Sewing	Finishing	Packaging and Shipping	Profit/Glove
Regular model	1	1/2	1/8	$5
Catcher's model	3/2	1/3	1/4	$8

a) Write the full Linear Programming model.

b) Solve using Excel Solver and paste your solution below, solving for the optimal solution (Max Profit). (HINT: your pasted answer should look similar to the output seen in Figure 2.26 on page90.)

Inputs/equation set up
Max Profit

Problem 5

A manufacturing company is considering expanding its production capacity to meet a growing demand for its product line of air fresheners. The alternatives are to build a new plant, expand the old plant, or do nothing. The marketing department estimates a 35 percent probability of a market upturn, a 40 percent probability of a stable market, and a 25 percent probability of a market downturn. Georgia Swain, the firm's capital appropriations analyst, estimates the following annual returns for these alternatives:

?	Market Upturn	Stable Market	Market Downturn
?
Build new plant	$690,000	$(130,000)	$(150,000)
Expand old plant	490,000	(45,000)	(65,000)
Do nothing	50,000	0	(20,000)

a. Use a decision tree analysis to analyze these decision alternatives.
b. What should the company do?
c. What returns will accrue to the company if your recommendation is followed?

Problem 6

A&C Distributors is a company that represents many outdoor products companies and schedules deliveries to discount stores, garden centers, and hardware stores. Currently, scheduling needs to be done for two lawn sprinklers: the Water Wave and Spring Shower models. Requirements for shipment to a warehouse for a national chain of garden centers are shown below.

Month	Shipping Capacity	Product	Minimum Requirement	Unit Cost to Ship	Per Unit Inventory Cost
March	8000	Water Wave	3000	.30	.06
		Spring Shower	1800	.25	.05
April	7000	Water Wave	4000	.40	.09
		Spring Shower	4000	.30	.06
May	6000	Water Wave	5000	.50	.12
		Spring Shower	2000	.35	.07

Let Sij be the number of units of sprinkler i shipped in month j, where i = 1 or 2, and j = 1, 2, or 3. Let Wij be the number of sprinklers that are at the warehouse at the end of a month, in excess of the minimum requirement.

a. Write the portion of the objective function that minimizes shipping costs.

b. An inventory cost is assessed against this ending inventory. Give the portion of the objective function that represents inventory cost.

c. There will be three constraints that guarantee, for each month, that the total number of sprinklers shipped will not exceed the shipping capacity. Write these three constraints.

d. There are six constraints that work with inventory and the number of units shipped, making sure that enough sprinklers are shipped to meet the minimum requirements. Write these six constraints.

Attachment:- Decision Making assignment.rar