The total cost for a manufacturing company is C(q)=1/30 q^3-3/10 q^2+q, where q is the quantity of output produced and C(q) is the cost in dollars. Find the quantity at which the company will minimize the average variable cost. What is the minimum average variable cost?

The management of Thermomaster Company, has estimated that the total weekly cost (in dollars) for producing x thermometers is C(x) = 8000 + 5x dollars per year. Find the average cost function C

The total cost to manufacture and sell q exactotherms is given by the cost equation C(q) = 2000+5q. The revenue equation is R(q)= 40q - 0.05q^2 dollars for the sale of q exactotherms. Assume the profit is P(q)= R(q) - C (q).   Find the number of items q to sell so that the profit function P(q) has its maximum.    Find on which interval(s) the profit function is increasing and decreasing.

Suppose the cost incurred in operating a cruise ship per hour is a+bv^33 dollars, where aand b are positive constants and v is the ship’s speed in miles per hour. At what speedshould the ship be operated between two ports (located d miles apart) to minimize thecost?