A company manufactures and sells x VCRs per month. If the cost and revenue equations are C(x) = 200 + 2x, R(x) = 20x − (x^2/50) , use differentials to estimate the change, ∆P, in profit when the production is increased from 100 to 101.

ΔP  = 14

Step-by-step explanation:

Given

Required

Determine the change in profit

First, we need to determine the profit

Collect Like Terms

Differentiate wrt x

When Profit increases from 100 to 101, the change becomes

ΔP  Δx

Δx

Where

So, the expression: ΔP  Δx becomes

ΔP  

ΔP  

ΔP  

ΔP  

ΔP  = 14