Question $12,1\mathrm{.}8\mathrm{.}29-$BE

Part $1$ of $4$

points

rk $3$

Points: $0$ of $1$

Consider the cost function $C(x)=6x^2+12x+16($thousand dollars$).$

a$)$ What is the marginal cost at production level $x=6?$

b$)$ Use the marginal cost at $x=6$ to estimate the cost of producing $6\mathrm{.}50$ units.

c$)$ Let $R(x)=-x^2+36x+32$ 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 the revenue is equal to the 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?

a$)$ The marginal cost at production level $x=6$ is $