Question

Find the rate of change of total​ revenue, cost, and profit with respect to time. Assume that​ R(x) and​ C(x) are in dollars. ​R(x)equals2 x​, ​C(x)equals0.01 x squared plus 0.3 x plus 30​, when xequals30 and StartFraction dx Over dt EndFraction equals9 units per day

Answer 1

Explanation:

Given the Total revenue R(x) = 2x

Cost C(x) = 0.01x²+0.3x+30 where;

x = 30 and dx/dt = 9units per day.

Rate of change of revenue dR/dt = dR/dx • dx/dt

dR/dt = 2dx/dt

dR/dt = 2(9) = $18

Rate of change of revenue with respect to time is 18dollars/day.

Rate of change of cost dC/dt = dC/dx • dx/dt

dC/dt = (0.02x+0.3)dx/dt

dC/dt at x = 30 and dx/dt = 9 will give;

dC/dt = {0.02(30)+0.3}×9

dC/dt = (0.6+0.3) × 9

dC/dt = 0.9×9

dC/dt = $8.1

Rate of change of cost with respect to time is 8.1dollars/day

Profit = Revenue - Cost

Profit = 18-8.1

Daily Profit = $9.9