Your new factory is at full production and with improved eff

Your new factory is at full production, and with improved efficiency, you want to ensure you have the best pricing for your product. Marketing tells you that monthly demand is currently modeled by the equation q = -350_p + 19600. Include units in your answers. Write a quadratic revenue function. Determine the optimal price to maximize revenue. How many would you sell at that price? Report the monthly revenue. A company that sells bobble-head dolls has found that they can sell 30 dolls each week if the price is $15 and 100 dolls each week if the price is $10. Construct the linear demand function, q = mp + b.

Solution

q = -350p + 19600

Rewriting to get price p, : p = (19600 - q)/350

Now Revenue function :R(q) = q*p = q(19600 - q)/350

= -q^2/350 + 19600q/350

To maximize reeny , find vertex of quadratic function :

q = - (19600/2*350) = 28

price , p = (19600 - q)/350 = (19600 -28)/350 =$ 55.92

We would sell 28 at this price

Total revenue = $55.92*28 = $1565.76