Mathematics 10 — Exercise 2.7 · Q6

Full question

Weekly earnings are E(h) = −2h² + 40h rupees. How many hours maximize earnings?

Step-by-step solution

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

   $$y=-2\times x^2+40\times x$$

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

   $$x=-\frac{40}{-4}$$

3. Simplify the division.

   $$x=10$$

4. Substitute this input back into the expression.

   $$y=200$$

5. Evaluate the output and include the required units.

   $$y=200$$

Answer

10 hours per week; maximum earnings Rs.200.