A division of Ditton Industries manufactures a deluxe toaster oven. Management h

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) = 0.0009x2 ? 0.18x + 22 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. (a) Find the total cost incurred by Ditton in producing the first 300 units of these toaster ovens per day. (b) What is the total cost incurred by Ditton in producing the 201st through 300th units/day?

Explanation / Answer

a. we have is total cost=800+integration(0 to 201)[0.0003x^2-0.12x+20] total cost=800+?(0 to 201)[0.0003x^2-0.12x+20]dx total cost=800+[0.0003x^3/3-0.12x^2/2+20x] (limits of 0 & 201 ie put 201 & 0 as x in the formula) total cost=800+[0.0001*210^2-0.06*201^2+20*201… total cost=3208.0001(approx 3208) b. additional revenue= total revenue at 300- total revenue at 200 additional revenue=?(0 to 300)[-0.1x+40]dx-?(0 to 200)[-0.1x+40]dx additional revenue=[-0.1x^2/2+40x](limits 0 and 300)-[-0.1x^2/2+40x](limits 0 and 200) additional revenue={[-0.1/2*300^2+40*300]-[0]}-{[-0… additional revenue=[12000]-[6000] additional revenue=6000 Hope i am correct as i solved these long time back. :)

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