Theory question 103
DifferentiationA company installs solar panels in its premises to reduce its electricity cost. The monthly savings on electricity in $, is modelled by S = 200 + 50x − 2x2, where x is the number of months after installation (a) At what time will the savings on electricity stop increasing? (b) Find the maximum savings.
Show the model answer
Model answer
(a) dS/dx = 50 − 4x = 0 ⇒ x = 12.5 months (12½ months after installation)
(b) S = 200 + 50(12.5) − 2(12.5)² = 200 + 625 − 312.5 = $512.50
Explanation
Savings stop increasing where the gradient dS/dx is zero.