Mathematics 10 — Exercise 2.7 · Q2

Full question

Profit P(x) = −5x²+150x−1000 (thousands of rupees), where x is price per item in rupees. Find the price giving maximum profit.

Step-by-step solution

1. The squared coefficient is negative, so the graph opens downward and its vertex is the maximum.

   $$y=-5\times x^2+150\times x-1000$$

2. Find the vertex input x = −b/(2a). Substitute the coefficient values.

   $$x=-\frac{150}{-10}$$

3. Simplify the division.

   $$x=15$$

4. Substitute this input back into the expression.

   $$y=125$$

5. Evaluate the output and include the required units.

   $$y=125$$

Answer

Price = Rs.15; maximum profit = Rs.125,000.