Question

The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 − 𝑥). Find x for which profit is increasing

Answer 1

Now, Profit = Revenue − Total cost

∴ π = R − C

= 240x − x² − (180 + 4x)

= 240x − x² − 180 − 4x

∴ π = − x² + 236x − 180 

∴ ${\displaystyle \frac{\text{d}\pi }{\text{d}x}}$ = −2x + 236 = 2(− x + 118)

Since profit is an increasing function, ${\displaystyle \frac{\text{d}\pi }{\text{d}x}}$ > 0

∴ 2(−x + 118) > 0

∴ − x + 118 > 0

∴ 118 > x

∴ x < 118

∴ The profit is increasing for x < 118.