Marginal Cost Analysis Consider the cost function C(x) = 6x2 + 14x + 18 (thousand dollars).
(a) What is the marginal cost at production level x = 5?
(b) Estimate the cost of raising the production level from x = 5 to x = 5.25.
(c) Let R(x) = −x2 + 37x + 38 denote the revenue in thousands of dollars generated from the production of x units. What is the break-even point? (Recall that the break-even point is when revenue is equal to cost.)
(d) Compute and compare the marginal revenue and marginal cost at the break-even point. Should the company increase production beyond the break-even point? Justify your answer using marginals.
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