Explore BrainMass
Share

Explore BrainMass

    Revenue and Cost

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com October 10, 2019, 3:48 am ad1c9bdddf
    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