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The histogram of best (i.e., lowest) competing bids in Table B of Problem 11 mirrors closely a normal distribution with a mean of 60 and a standard deviation of 30. Create a spreadsheet modeled on the sample given to find the firm's optimal bid markup. In the sample spreadsheet, note that a bid at a 60 percent markup has a .5 chance of winning and implies an expected profit of (.5)(60) = 30.a. First, experiment with other markups in your search for maximum expected profit.b. Use your spreadsheet's optimizer to find the optimal markup.c. Find the firm's optimal markups if the BCB distribution has a (less favorable) mean of 40 or if it has a (more favorable) mean of 80.
A
B
C
D
E
F
G
H
1
2
OPTIMAL STRATEGY WHEN BCB
3
IS NORMALLY DISTRIBUTED
4
5
Mean =
60
Markup
Pr(win)
E(Profit)
6
St Dev =
30
7
20
0.9088
18.176
8
40
0.7475
29.900
9
0.5000
30.000
10
80
0.2525
20.199
11
12
(Hint: Cells F7 to F10 should be computed utilizing the normal distri- bution function included with your spreadsheet. This function typi- cally takes the form:Normal(value, mean, standard deviation).Thus, you can simply change the value of the mean in cell C5 to 40 or 80 and reoptimize the problem.)
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