# Revenue and Cost

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?

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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.