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A company knows that unit cost C and unit revenue R from the production and sale of x units are related by C=R^2/100,000 + 3064. Find the rate of change of revenue per unit when the cost per unit is changing by $11 and the revenue is $4000.

Sagot :

Answer:

The rate of change of revenue per unit is $137.50.

Explanation:

Given;

C = R^2/100,000 + 3064 = (1/100,000)R^2 + 3064 = 0.00001R^2+ 3064 ............ (1)

Differentiating equation (1) with respect to x, we have:

dC/dx = (2 * 0.00001)R * dR/dx

dC/dx = 0.00002R * dR/dx ,,,,,,,,,,,,,,,,,,,, (2)

Where;

dC/dx = Change in cost per unit = $11

R = Revenue = $4000

dR/dx = the rate of change of revenue per unit = ?

Substituting the relevant values into equation (2) and solve for dR/dx, we have:

11 = (0.00002 * 4000) * dR/dx

11 = $0.08 * dR/dx

dR/dx = 11 / 0.08

dR/dx = 137.50

Therefore, the rate of change of revenue per unit is $137.50.

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