A company marketing research Department recommended to the Administration, to manufactures and merchandises a promising product. After extensive surveys, the Department of investigation gave its recommendation with the demand equation: x = f (p) = 6000-30 p where x is the number of units that retailers may be purchased for $ p per unit. From the Finance Department, the following cost equation was obtained: C = g (x) = 72,000 + 60 x where $72,000 is the fixed cost (tools and overload) and $60 is the variable cost per unit (materials, marketing, transportation, storage, etc.).
1. Express the demand equation x = f (p) = 6000-30 p in terms of the variable x. (Hint: solved for p, in other words, solve the equation x = 6000-30 p in terms of the variable p with respect of x.)
2.Find the revenue function R (x).
3. Find the number of units that the company should produce in order to obtain the maximum income.