See communications exercise. If a cost function is given by: C(x) = 2x^2 + 225x
ID: 2878166 • Letter: S
Question
See communications exercise. If a cost function is given by: C(x) = 2x^2 + 225x + 5000, find the number of items for which average is at a minimum. The demand equation for a product is p = 100 - 0.5x. The Cost function is given by C(x) = 2x^2 + 5x + 18. Find the number of items that produce maximum profit. A model for the amount of time it takes for the first customer to arrive at a diner is: f(x) = 1/6 e - x/6 x = minutes after opening; f(x) = probability a) Find the probability that the first customer arrives in the first 5 minutes. b) Find the probability that the first customer arrives between the 2^nd and 5^th minute. In both answers, compute the probability to three decimal places. For the following functions: Demand: D(x) = 13-x Supply: S(x) = x^2 + 1 Find the equilibrium point, consumer's surplus and producer's surplus.Explanation / Answer
(2) C(x) = 2x^2 + 255x + 5000
Average cost AC(x) = 2x + 255 + 5000/x
AC'(x) = 2 + (255/x) - 5000/(x^2)
For AC to be minimum, AC'(x) = 0
2 + (255/x) - 5000/(x^2) = 0
2x^2 + 255x - 5000 = 0
Upon solving this, we get x = {-144.77, 17.27}
Number of items for which average cost is a minimum is x = 17.27 (say 17)