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# Revenue and Cost

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Mr. Mick Mouse has a trap company with fixed costs of \$846 variable (ie: operating) costs of \$2 per trap and a demand curve of: traps=116-2(price). Since Mick doesn't understand economics find the revenue and cost functions in terms of price for his business.

a) Graph these two functions over the price domain. Find the breakeven point and the profit at the highest price possible. What does this relationship mean for his business?

b) Construct the profit function and list the key points or roots of the function. What happens to profit as Mick increases his price?

c) Using any method discussed in class compute the maximum profit and the appropriate price to charge to achieve this value. What quantity of traps should he produce and what would it cost to produce these traps?

https://brainmass.com/math/calculus-and-analysis/revenue-and-cost-435824

#### Solution Preview

Please see either of the attached files (word, excel). Both contain the answers
9. Mr. Mick Mouse has a trap company with fixed costs of \$846 variable (ie:
operating) costs of \$2 per trap and a demand curve of: traps=116-2(price). Since Mick doesn't understand economics find the revenue and cost functions in terms of price for his business.

Let the Price be denoted by P and Quantity demanded by Q

Demand curve says that Q= 116 - 2 P

Revenue = PQ = P (116- 2P)= 116 P - 2 P^2
(^ = raised to the power of)

Costs:
Variable Cost = 2 Q = 2 (116-2P) =232 - 4P
Fixed Cost = 846
Total Cost= 232- 4P + 846 = 1078-4P

Thus
Revenue Function= R= 116 P - 2 P^2
Cost Function = C = 1078 - 4P

a) Graph these two functions over the price domain. Find the breakeven
point and the profit at the highest price possible. What does this relationship mean for his business?

Price Revenue Cost Profit (Revenue-Cost)
1 114 =116 x 1 - 2 x1^2 1074 =1078 - 4 x 1 -960 =114 - 1074
2 224 =116 x 2 - 2 x2^2 1070 =1078 - 4 x 2 -846 =224 - 1070
3 330 =116 x 3 - 2 x3^2 1066 =1078 - 4 x 3 -736 =330 - 1066
4 432 =116 x 4 - 2 x4^2 1062 =1078 - 4 x 4 -630 =432 - 1062
5 530 =116 x 5 - 2 x5^2 1058 =1078 - 4 x 5 -528 =530 - 1058
6 624 =116 x 6 - 2 x6^2 1054 =1078 - 4 x 6 -430 =624 - 1054
7 714 =116 x 7 - 2 x7^2 1050 =1078 - 4 x 7 -336 =714 - 1050
8 800 =116 x 8 - 2 x8^2 1046 =1078 - 4 x 8 -246 =800 - 1046
9 882 =116 x 9 - 2 x9^2 1042 =1078 - 4 x 9 -160 =882 - 1042
10 960 =116 x 10 - 2 x10^2 1038 =1078 - 4 x 10 -78 =960 - 1038
11 1034 =116 x 11 - 2 x11^2 1034 =1078 - 4 x 11 0 =1034 - 1034
12 1104 =116 x 12 - 2 x12^2 1030 =1078 - 4 x 12 74 =1104 - 1030
13 1170 =116 x 13 - 2 x13^2 1026 =1078 - 4 x 13 144 =1170 - 1026
14 1232 =116 x 14 - 2 x14^2 1022 =1078 - 4 x 14 210 =1232 - 1022
15 1290 =116 x 15 - 2 x15^2 1018 =1078 - 4 x 15 272 =1290 - 1018
16 1344 =116 x 16 - 2 x16^2 1014 =1078 - 4 x 16 330 =1344 - 1014
17 1394 =116 x 17 - 2 x17^2 1010 =1078 - 4 x 17 384 =1394 - 1010
18 1440 =116 x 18 - 2 x18^2 1006 =1078 - 4 x 18 434 =1440 - 1006
19 1482 =116 x 19 - 2 x19^2 1002 =1078 - 4 x 19 480 =1482 - 1002
20 1520 =116 x 20 - 2 x20^2 998 =1078 - 4 ...

#### Solution Summary

Calculates breakeven, graphs revenue and cost functions.

\$2.19