In below Problems cost, revenue, and profit are in dollars and x is the number of units.
1. Suppose the total cost function for a product is C(x) = 3x2 + 15x + 75 How many units will minimize the average cost? Find the minimum average cost.
2. Suppose the total revenue function for a product is given by R(x) = 32x - 0.01 x2
(a) How many units will maximize the total revenue? Find the maximum revenue.
(b) If production is limited to 1500 units, how many units will maximize the total revenue? Find the maximum revenue.
3. Suppose the profit function for a product is P(x) = 1080x + 9.6x2 - 0.1x3 - 50,000 Find the maximum profit
4. How many units (x) will maximize profit if R(x) = 46x - 0.01x2 and C(x) = 0.05x2 + 10x + 1100?
5. A product can be produced at a total cost of C(x) = 800 + 4x, where x is the number produced and is limited to at most 150 units. If the total revenue is given by R(x) = 80x - 1/4x2, determine the level of production that will maximize the profit.