Suppose that the monthly cost, in dollars, of producing x chairs isC(x)=0.005x3+0.07x2+18x+700, and currently 50 chairs are produced monthly. a)What is the current monthly cost?b)What is the marginal cost whenx=50?c)Use the result from part (b) to estimate the monthly cost of increasing production to52 chairs per month.d)What would be the actual additional monthly cost of increasing production to52 chairs monthly?

We will use derivative to find marginal cost a) Current monthly cost given by C(x)=0.005x3+0.07x2+18x+700 As currently 50 chairs are produced => x=50 C(50)=0.005×503+0.07×502+18×50+700= 2400 Current monthly cost = 2400 $ b) For marginal cost differentiate C(x) C'(x)=0.005ddxx3+0.07ddxx2+18ddxx+700MC(x) = C'(x)=0.005×3x2+0.07×2x+18×1At x=50 MC(50) =0.005×3× 502+0.07×2×50+18 =62.5 So marginal cost when 5o item are produced = 62.5 $c) Marginal cost represent increase in cost when one more chair is produced from the number of chair already producing . Here marginal cost at x=50 in 62.5$ which indicate when one more chair is produced from current level of 50 chairs then cost will be increased by 62.5 $ . When 2 more chairs produced then cost increase by 2 ×62.5 $ = 125$ So total cost of producing 52 chairs -C(50) +125=2400+125= 2525$ d) Actual increase in monthly cost C52-C50=0.005×523+0.07×522+18×52+700-2400=2528.32-2400= 128.32 Actual increase = 128.32 $

Answered: Suppose that the monthly cost, in…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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a)	What is the current monthly cost?
b)	What is the marginal cost when x=50?
c)	Use the result from part (b) to estimate the monthly cost of increasing production to 52 chairs per month.
d)	What would be the actual additional monthly cost of increasing production to 52 chairs monthly?