Question

A contractor has found that her cost for a certain construction job is subject to random variation. She believes its actual value follows a continuous uniform distribution between $9000 and $11000 with a mean of $10,000. The cost to prepare her bid is $500. She is competing in a sealed bid competition with four other contractors. She believes that the bids submitted by the other contractors will vary triangularly with a minimum equal to her minimum cost, a most likely value equal to her 1.3 times her mean cost and a maximum equal to 2.5 times her mean cost and that their bids are independent of each other. She will win the competition if her bid is smaller than the bids of all four competitors. If she wins, her profit will be the difference between her bid and her cost minus the proposal preparation cost. If she loses her proposal preparation cost is lost and her profit is -$500. Simulate 1000 bids in which her bid amount is $14,000 and determine the distribution of her profit. Include the histogram in your response. Also determine the probability that she wins the competition and the probability that she loses money. Compare these results for bid amounts of $13000 and $15000

Answer 1

Attached is the profit distribution plotted on the chart and also the detailed solution using excel

Explanation:

To solve this problem we have to

• create a column for number of counts ( 1,2,3........1000) bids
• create a column for the cost to be incurred which is mostly dependent on the random number generated. the formula for that using excel is; 9000+ rand()*(11000-9000) for uniform distribution between the numbers
• Four(4) more columns are generated for bids of competitors by using the formula: 10000+rand()*(3*10000-10000) this because the bids that will be submitted by others bidders will vary uniformly between her mean cost and 3 times her mean cost
• Condition is checked to see if the lowest bid is. =IF(MIN(the 4 bids)>14000,1,0)
• Next the same process is carried out for 13000 and 15000
• The probability of winning is calculated in excel using this formula =Countif(value of step 4 for all the rows,1)/1000