Question

A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that the daily marginal cost function associated with producing these toaster ovens is given by C'(x) = 0.0003x^2 - 0.12x + 23 where C'(x) is measured in dollars/unit and x denotes the number of units produced. Management has also determined that the daily fixed cost incurred in the production is $800. Find the total cost incurred by Ditton in producing the first 300 units of these toaster ovens per day. What is the total cost incurred by Ditton in producing the 201st through 300th units/day?

Answer 1

a)total cost =800+∫_{[0 to 300]}[0.0003x^2 -0.12x+23]

=800+_{[0 to 300]}[0.0001x^3 -0.06x^2 +23x]

=800+ [(0.0001*300^3 -0.06*300^2 +23*300)-(0.0001*0^3 -0.06*0^2 +23*0)]

=800+4200

=5000 $

b)total cost incurred by ditton in producing 201st through 300th units/day=∫_{[200 to 300]}[0.0003x^2 -0.12x+23]

=_{[200 to 300]}[0.0001x^3 -0.06x^2 +23x]

=[0.0001*300^3 -0.06*300^2 +23*300]-[0.0001*200^3 -0.06*200^2 +23*200]

= [4200-3000]

=1200 $