Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost: r(x) = 30x - 0.5x 2 c(x) = 2x + 8. 9) a) 32 units b) 36 units

The profit is maximum when 28 units are sold.

Step-by-step explanation:

The given revenue function is

The given cost function is

Profit is the difference of revenue and cost. So the profit function is

On combining like terms, we get

It is a quadratic function. Leading coefficient is negative so it is a downward parabola. Vertex of a downward parabola is the point of maxima.

If a quadratic function is , then the vertex of the parabola is

In the profit function a=-0.5, b=28 and c=-8, the function is maximum at

Therefore the profit is maximum when 28 units are sold.

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

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