The daily cost to manufacture trinkets for tourists is given by the cost functio
ID: 3264252 • Letter: T
Question
The daily cost to manufacture trinkets for tourists is given by the cost function
C(x)=0.002x^2+4.7x+700 dollars
where x is the number of trinkets.
a. Use CALCULUS to estimate the cost of the 258th trinket. How does this compare with the EXACT cost of producing the 258th trinket? Include correct units. Do not round values.
b. If the trinkets sell of $5.50 each, report the revenue and profit functions.
c. For which value is marginal profit zero? Interpret your answer. Include correct units. What is the significance of the point where the marginal profit is zero?
Explanation / Answer
1)a)
calculas
dC(x)/dx = 0.002*2*x + 4.7
= 4.7 + 0.004*258
= 5.732
Exact answer = C(258) -C(257)
= (0.002*258^2 +4.7*258 +700) - (0.002*257^2 +4.7*257 +700)
= 5.73
b) Revenue = 5.5*x
Profit = Revenue - Cost
= 5.5x- (0.002x^2+4.7x+700)
c) marginal profit = marginal revenue - marginal cost
= R' - C'
= 5.5 - (0.004*x +4.7)
= 0.8 - 0.004*x
Mp = 0 or x = 0.8/0.004 = 200
a firm should continue to produce a good or service up to the point where marginal profit is zero
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