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.

Asked on by rodrigozz

1 Answer | Add Yours

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violy | High School Teacher | (Level 1) Associate Educator

Posted on

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.

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