Math / Calculus

Question107 Assignment 11: Problem 6 (1 point)
Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by $C=70000+40 x, \quad R=400-\frac{x^{2}}{20}$ where the production output in one week is $x$ calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:
Rate of change in cost $=$ 20000 $\square$ Rate of change in revenue $=-20000$ $\square$ Rate of change in profit $=-24000$ $\square$

Studdy Solution
The profit $P$ is given by $P = R - C$ .
Differentiate the profit equation with respect to time $t$ :
$\frac{dP}{dt} = \frac{dR}{dt} - \frac{dC}{dt}$
Substitute the values from the previous steps:
$\frac{dP}{dt} = -100000 - 20000 = -120000$
The rates of change are:
Rate of change in cost $= 20000$
Rate of change in revenue $= -100000$
Rate of change in profit $= -120000$

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