Rose\'s Confections manufactures and sells x pounds of fudge per week. The month
ID: 2878241 • Letter: R
Question
Rose's Confections manufactures and sells x pounds of fudge per week. The monthly cost and price-demand equations are C(x) =1,500 + 4x, p(x) = 40 (x/3) where C is the total cost of producing x pounds of fudge that sell for p dollars each. Show your work.
a) Find the revenue function.
answer:
b) Find the marginal revenue function.
answer:
c) Use the marginal revenue function to approximate the additional revenue that would result from selling the 52nd pound of fudge.
answer:
d) Find the (exact) additional revenue that would result from selling the 52nd pound of fudge.
answer:
Explanation / Answer
cost C(x) =1,500 + 4x, price p(x) = 40 (x/3)
a) revenue R(x) =p*x
R(x) =( 40 (x/3) )*x
R(x) =40x (x2/3)
b)marginal revenue R'(x)=40- (2x/3)
c)additional revenue that would result from selling the 52nd pound of fudge =R'(51) =40- (2*51/3) =6 dollars
d) (exact) additional revenue that would result from selling the 52nd pound of fudge =R(52)-R(51)
=[40*52 (522/3) ]-[40*51 (512/3) ]
=[2080 (2704/3) ]-[2040 (2601/3) ]
=17/3
=5.67 dollars
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