The cost of producingx units is given by C(x) = 32000 + 1.7x + 20x dollars. Find the value of x that minimizes the average cost function if IsxS 62.
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- How are the absolute maximum and minimum similar to and different from the local extrema?A manufacturer has determined that the total cost C of operating a factory is C = 1.5x2 + 45x + 15000, where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.) x=? unitsN Communications provides cellular telephone services. The company is planning to expand into the Cincinnati area and is trying to determine the best location for its transmission tower. The tower transmits over a radius of 10 miles. The locations that must be reached by this tower are shown in the following figure. x y Florence 18 12 Covington 12 16 Hyde Park 16 18 Evendale 12 22 TN Communications would like to find the tower location that reaches each of these cities and minimizes the sum of the distances to all locations from the new tower. Round your answers to two decimal digit. (a) Formulate and solve a model that minimizes the total distance between the transmission tower location and all the city locations. x y Tower location 14.77 17.38 Max Distance miles (b) Formulate and solve a model that minimizes the maximum distance from the transmission tower location to the city locations. x y Tower location 15 Max Distance 5.8 miles
- Joe owns a coin that is either a fair coin or a two-headedcoin. Imelda believes that there is a 12chance that the coinis two-headed. She must guess what kind of coin Joe has. Ifshe guesses correctly, she pays Joe nothing, but if sheguesses incorrectly, she must pay Joe $2. Before guessing,she may pay 30¢ to see the result of a single coin toss (headsor tails). Determine how Imelda should minimize herexpected loss. Also determine EVSI and EVPI.At noon, ship A is 45 miles south of Ship B. Ship A is sailing north at a rate of 15 miles per hour. Ship B is sailing west at a rate of 15 miles per hour. When is the distance between the two ships minimized? In the field below enter the time at which the distance between the ships is minimal.A manufacturer has determined that the total cost C of operating a factory is C = 0.5x2 + 15x + 5000 where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)
- 3. Where is p(x) the worst approximation to r(x)? In other words, where is the vertical distance between the two functions maximized?Let C (x)=1/2x^3-5x^2+20x be the cost function of producing a phone case. Where x is the amount of phone cases in hundred and C9x) is in thousand dollars. a) Use the formula for the average cost, A(x)= C(x)/x, to find the average cost function. b) Find the point where the AVERAGE COST is minimized.