1.Cedar Point amusement park management is preparing the park\'s annual promotio
ID: 351769 • Letter: 1
Question
1.Cedar Point amusement park management is preparing the park's annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. Given an advertising budget of $125,000, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem to be solved using QM.
Type
Cost
Maximum number
Exposure (1000s)
Newspaper
750
50
40
Television
1100
25
60
Radio
325
25
22.5
Shows
75
1.5
5
2.A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120, while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed six times the number of tables. How many tables and chairs should the furniture manufacturer produce to maximize profit?
3.East Valve Distributors distributes industrial valves and control devices. The Eastern control device has an annual demand of 9,000 units and sells for $90 per unit. The cost of ordering is $150 per order and the average carrying cost per unit per year is $0.85. Determine the economic order quantity.
4.Furniture Manufacturers Inc., uses 10,000 loads of lumber per year. A load of lumber costs $250 and the carrying cost is 10 percent of the unit cost. The cost to order is $100 per order and the leadtime is three working days. Assuming 100 working days, determine:
(a) the economic order quantity.
(b) the reorder point.
(c) number of orders per year.
(d) working days between orders.
5.Demand for local newspapers in King County during weekdays is normally distributed with a mean of 500 and standard deviation of 100. The marginal loss per paper is $0.20 and marginal profit is $0.80. How many newspapers should the local publisher produce each day?
6.Consider the material structure tree for item A below. Assume 15 units of A are needed.
(a) How many units of B are needed?
(b) How many units of C are needed?
(c) How many units of D are needed?
(d) How many units of E are needed?
Type
Cost
Maximum number
Exposure (1000s)
Newspaper
750
50
40
Television
1100
25
60
Radio
325
25
22.5
Shows
75
1.5
5
Explanation / Answer
PLEASE FIND BELOW ANSWERS TO QUESTION NUMBERS #3, #4 AND #5 :
Answer to question number 3 :
Given are following data :
Annual demand = D = 9000 units
Ordering cost = Co = $150 per order
Average carrying cost per unit per year = Ch =$0.85
The Economic Order Quantity ( EOQ)
= Square root ( 2 x Co x D/ Ch )
= Square root ( 2 x 150 x 9000/ 0.85)
= 1782.26 ( 1782 rounded to nearest whole number )
ECONOMIC ORDER QUANTITY = 1782
Answer to question number 4 :
Annual demand = D = 10,000 loads of lumber
Daily demand = d = Annual demand / Working days = 10,000/100 = 100
Ordering cost = Co = $100 / order
Annual unit inventory cost = Ch = 10 percent of $250 = $25
The economic order quantity ( EOQ )
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 100 x 10,000/ 25)
= 282.84 ( 283 rounded to nearest whole number )
ECONOMIC ORDER QUANTITY = 283 LOADS OF LUMBER
Number of orders per year = Annual demand / EOQ = 10,000 / 283 =35.33 on average
Working days between orders = EOQ/ Daily demand = 283/100 = 2.83 days
NUMBER OF ORDERS PER YEAR = 35.33
WORKING DAYS BETWEEN ORDERS = 2.83 DAYS
The Reorder point = Daily demand x Lead time ( working days ) = 100 x 3 = 300 loads of lumber
REORDER POINT = 300 LOADS OF LUMBER
Answer to question 5 :
We can define Critical ratio as :
Critical ratio = Marginal profit / ( Marginal profit + Marginal loss) = 0.8 / ( 0.8 + 0.2) = 0.8
Critical ratio is the probability of the optimum production quantity per day .
Therefore , probability of optimum production quantity = 0.8
Corresponding Z value = NORMSINV ( 0.8 ) = 0.8416
Quantity of newspaper to be produced everyday
= Mean daily demand + Z value x Standard deviation of daily demand
= 500 + 0.8416 x 100
= 500 + 84.16
= 584.16 ( 584 rounded to nearest whole number )
LOCAL PUBLISHER SHOULD PRODUCE584 NEWSPAPER EVERYDAY
ECONOMIC ORDER QUANTITY = 1782
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