Suppose the cost per hour incurred in operating a cruise ship is 3a + bv3 dollars per hour, where a and b are positive constants and v is the ship's speed in miles per hour. At what speed (in miles per hour) should the ship be operated between two ports, at a distance D miles apart, to minimize the cost? (Hint: Minimize the cost, not the cost per hour.)

Suppose the cost per hour incurred in operating a cruise ship is 3a + b dollars per hour, where a and b are positive constants and v is the ship's speed in miles per hour. At what speed (in miles per hour) should the ship be operated between two ports, at a distance D miles apart, to minimize the cost? (Hint: Minimize the cost, not the cost per hour.)

The speed at which the ship would maximize cost is

Explanation:

The problem can be solved using differentiation to get the minimum value of the speed to travel between the two ports. Step by step calculation is contained in the attached images;

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a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.