hi, i\'d like help with this please (3 pts) Example 2.5.1 A manufacturer estimat

Question

hi, i'd like help with this please

(3 pts) Example 2.5.1 A manufacturer estimates that whenxlunits of a particular commodity are produced, the total cost will be C00 x2 6x 90 dollars, and furthermore, that all xl units will be sold when the price is pCO (70 x) dollars per unit a. Find the marginal cost and the marginal revenue. The marginal cost is C'C) 2/3x+6 and the marginal revenue is 2/3x+7 b. Use marginal cost to estimate the cost of producing the 34th unit. What is the actual cost of producing the 34th unit? The cost of producing the 34th unit is the change in cost xlincreases from 33 to 34 and can be estimated by the marginal cost when producing 33 units: C' (33) dollars. The actual cost of producing the 34th unit is C(34) C(33) dollars c. Use marginal revenue to estimate the revenue derived from the sale of the 34th unit. What is the actual revenue derived from the sale of the 34th unit? The revenue obtained from the sale of the 34th unit is approximated by the marginal revenue atx 33: R (33) dollars. The actual revenue obtained from the sale of the 34th unit is R(34) R(33) dollars

Explanation / Answer

given cost C(x) =(1/3)x2+6x+90 ,p(x)=(1/3)(70-x)

revenue R(x)=px =(1/3)(70x-x2)

a)C(x) =(1/3)x2+6x+90

marginal cost C'(x) =(2/3)x+6

marginal revenue R'(x)=(1/3)(70-2x)=(70/3) -(2/3)x

b)C'(33) =(2/3)33 +6=22+6=28 dollars

C(34)-C(33)=[(1/3)342+6*34+90]-[(1/3)332+6*33+90]=85/3=28.33 dollars

c)R'(33)=(1/3)(70-2*33) =4/3 dollars

R(34)-R(33)=(1/3)(70*34 -342) -(1/3)(70*33 -332) =1 dollar

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