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- From: Mathematics, Statistics and Probability
- Posted on: Thu 21 Jan, 2016
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Problem 1
Print Media Advertising (PMA) has been given a contract to market Buzz Cola via newspaper ads in a major southern newspaper. Full-page ads in the weekday editions (Monday through Saturday) cost $2000, whereas on Sunday a full-page ad costs $8000. Daily circulation of newspaper is 30,000 on weekdays and 80,000 on Sundays.
PMA has been given a $40,000 advertising budget for the month of August. The experienced advertising executives at PMA feel that both weekday and Sunday newspaper ads are important; hence they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fractional ad would simply mean that a smaller ad is placed on one of the days; that is, 3.5 ads would mean three full-page ads and one half-page ad. Also, assume that smaller ads reduce exposure and costs proportionately.) This August has 26 weekdays and 5 Sundays.
The objective is to determine the optimal placement of ads by PMA in the newspaper during August so as to maximize the cumulative total exposure (as measured by circulation) for the month of August.
a) Formulate the linear programming model for the problem.
b) Use the Graphical method to find the optimal solution. Show all steps.
c) Use Excel Solver to find the optimal solution. Copy and paste your spreadsheet and the Answer report in its entirety from Excel. Remember to not delete/modify any part of the Answer Report.
Problem 2
Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Advance sales are so small that Weiss has no way to estimate the demand for the red roses. She buys roses for $15 per dozen and sells them for $40 per dozen. Pay-off table for the problem is given below.
Demand for Red Roses
Alternative Low (25 dozen) Medium (60 dozen) High (130 dozen)
Do nothing 0 0 0
Order 25 dozen 300,000 300,000 300,000
Order 60 dozen 100,000 600,000 600,000
Order 130 dozen -100,000 400,000 900,000
Probability 0.3 0.4 0.3
What is the decision based on each of the following criteria? Show work in making the decision for each criterion.
a) EMV approach b) EOL approach
Problem 3
Build-Rite construction has received favorable publicity from guest appearances on a public TV home improvement program. Public TV programming decisions seem to be unpredictable, so Build â€“Rite cannot estimate the probability of continued benefits from it relationship with the show. Demand for home improvements next year may be either low or high. But Build-Rite must decide now whether to hire more employees, do nothing, or develop subcontracts with other home improvement contractors. Build-Rite has developed the following payoff table.
Payoffs Demand For Home Improvements
Alternative Low Moderate High
Hire ($250,000) $100,000 $625,000
Subcontract $100,000 $150,000 $415,000
Do nothing $50,000 $80,000 $300,000
What is the decision based on each of the following criteria? Show work in making the decision for each criterion:
a) Maximax
b) Maximin
c) Criterion of realism with coefficient of realism = 0.7
d) Equally likely
e) Minimax regret
Problem 4
Planwell Corporation is considering whether to build a large plant or a small plant for new product, which has an estimated life of 7 years. A small plant requires an investment of $3.4 million and a large plant of $4 million. The following estimates are available for annual income.
Plant Size Demand Annual Income
Large High $900,000
Low $300,000
Small High $600,000
Low $500,000
The probability of high demand in first year is 0.75. If the demand is high in the first year, the probabilities of high and low demands in subsequent years are 0.7 and 0.3 respectively. The probability of low demand in the first year is 0.25. If the demand is low in the first year, the probabilities of high and low demands in subsequent years are 0.2 and 0.8 respectively.
Evaluate the decision alternatives open to the company using decision trees. Which alternative should be followed by the Planwell company and what return can be expected?
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