# The demand function for a product is p = 1000 - 2q Finding the level of production that maximizes total revenue producer, and determine that incomewhere p is the price (indollars) per unit when q...

**The demand function for a product is p = 1000 - 2q Finding the level of production that maximizes total revenue producer, and determine that income**

where p is the price (in

dollars) per unit when q units are

demand (per week) by

consumers.

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### 1 Answer

Take note that Revenue function (R(x)) is price times demand.

So, R(x) = (1000 - 2q)q = 1000q - 2q^2.

That is a quadratic function, which is in the form aq^2 + bq + c

where a < 0. Hence, the parabola opens downward. So, the maximum value will be found at the vertex.

So, we will solve for q, on vertex (q, r).

So, q = -b/2a = -1000/2(-2) = 250.

Hence, for **250 units per week**, there will be maximum revenue.

And for the maximum revenue, we will replace the q by 250 on our revenue function.

R(250) = 1000(250) - 2(250)^2 = 250000 - 125000 = **$125000**.