Question

Simulate the following decision situation for 20 weeks, and recommend the best decision.
A concessions manager at the Tech versus A&M football game must decide whether to have the
vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies,
and a 55% chance of sunshine, according to the weather forecast in college junction, where the
game is to be held. The manager estimates that the following profits will result from each decision,
given each set of weather conditions:
MAT540 Homework
Week 3
Page 3 of 3
Decision Weather Conditions
Rain
0.35
Overcast
0.25
Sunshine
0.40
Sun visors $-400 $-200 $1,500
Umbrellas 2,100 0 -800
5. Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either 1, 2,
or 3 hours are required to fix it, according to the following probability distribution:
Repair Time (hr.) Probability
1 0.20
2 0.50
3 0.30
1.00
Simulate the repair time for 20 weeks and then compute the average weekly repair time.

Answer 1

Answer:

There are 2 different set of weather conditions percentage given in the question. I am assuming the one in the paragraph(03%, 15%, 55%) as correct and solving this question accordingly.

Simulating the condition, the football game occurs once per week ie 20 times in 20 weeks.

Probability percentage for Rain is 30%. Therefore in 20 weeks on game days probability of rain occurrence = 20 X 30/100 = 6

Probability percentage for Overcast skies is 15%. Therefore in 20 weeks on game days probability of Over cast skies = 20 X 15/100 = 3

Probability percentage for Sunshine is 55%. Therefore in 20 weeks on game days probability of Sunshine= 20 X 55/100 = 11

Decision to buy Umbrella :

Profit = Number of times rain occurs X 2100 + Number of times Overcast X 0 + Number of times Sunshine occurs X (-800)

Profit = 6 X 2100 + 3 X 0 + 11 X (-800) = $3800

Decision to buy Sun Visors :

Profit = Number of times rain occurs X (-400) + Number of times Overcast X (-200) + Number of times Sunshine occurs X 1500

Profit = 6 X (-400) + 3 X (-200) + 11 X 1500 = $ 13,500

Looking at the profits made in both the cases, it can be concluded that buying Sun visors is more profitable and hence a better choice.