## Related questions with answers

Cost, revenue, and profit rates. Repeat Problem $33$ for

$\begin{aligned} C&=72,000+60x \quad R=200x-\frac{x^2}{30}\\ P&=R-C \end{aligned}$

where production is increasing at a rate of $500$ calculators per week at a production level of $1,500$ calculators.

Solution

VerifiedGiven the equations for the cost $(C)$, revenue $(R)$, and profit $(P)$ are

$\begin{aligned} C&= 60x+72,000\\ R&=\frac{6,000x-x^2}{30}\\ P&=\frac{6,000x-x^2}{30}-(60x+90,000) \end{aligned}$

Also, at a rate of $500$ calculators per week the production grows, that is,

$\dfrac{\text{d}x}{\text{d}t}=500$

and the output of the production is $6,000$ calculators, that is,

$x=1,500$

$(\text{A})$ Determine the rate of increase or decrease in cost, that is, $\dfrac{\text{d}C}{\text{d}t}.$

$(\text{B})$ Determine the rate of increase or decrease in cost, that is, $\dfrac{\text{d}R}{\text{d}t}.$

$(\text{C})$ Determine the rate of increase or decrease in cost, that is, $\dfrac{\text{d}P}{\text{d}t}.$

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