Answer to Question #148148 in Calculus for Sean

Question #148148

This week a factory is producing 50 units of a particular commodity, and the amount being

produced is increasing at the rate of 2 units per week. If 𝐢(π‘₯) dollars is the total cost of producing

π‘₯ units and 𝐢(π‘₯) = 0.08π‘₯^3 βˆ’ π‘₯^2 + 10π‘₯ + 4 , find the current rate at which the production cost is increasing.








1
Expert's answer
2020-12-07T18:32:01-0500

C(x)=0.08x3βˆ’x2+10x+48dCdx=0.24x2βˆ’2x+10dCdx∣x=2=0.24(2)2βˆ’2(2)+10=0.24Γ—4βˆ’4+10=0.96βˆ’4+10=6.96Therefore, the current rate atwhich the production costis increasing is  6.96dollars per units.C(x) = 0.08x^3 - x^2 + 10x + 48\\ \frac{\mathrm{d}C}{\mathrm{d}x} = 0.24x^2 - 2x + 10\\ \begin{aligned} \frac{\mathrm{d}C}{\mathrm{d}x}\biggr\vert_{x = 2} &= 0.24(2)^2 - 2(2) + 10 \\&= 0.24\times 4 - 4 + 10 \\&= 0.96 - 4 + 10 = 6.96 \end{aligned}\\ \textsf{Therefore, the current rate at}\\ \textsf{which the production cost}\\ \textsf{is increasing is}\, \, 6.96 \\ \textsf{dollars per units.}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment