4. A company has determined that the cost in dollars to manufacture x cases of its...

Question

Question

4. A company has determined that the cost in dollars to manufacture x cases of its product is given by TC(x)=100+20x-x^2 (0≤x≤6)

a. Find the average rate of change of manufacturing cost per case between 1 and 5 cases.

b. Find the instantaneous rate of change of manufacturing cost when the 3rd case is produced.

c. Find marginal cost (MC) at x = 3.

Answer 1

Answer #1

Cost is given by TC(x) = 100 + 20x - x^2

a. Change of manufacturing cost between 1 and 5 cases = [100 + 20*5 - 5^2] - [100 + 20*1 - 1^2]

= 56

Now average rate of change of manufacturing cost per case between 1 and 5 cases = 56/5 = 11.20

b. Instantaneous rate of change of manufacturing cost when the 3rd case is produced

= dTC/dx (at x = 3)

= (20 - 2x)(at x = 3)

= (20 - 6)

= $14

c. Marginal cost (MC) at x = 3

= dTC/dx (at x = 3)

= $14

Answer 2

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