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Let Q = (0, 3) and R = (10, 8) be given points in the plane. We want to find the point P = (x,

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Let Q = (0, 3) and R = (10, 8) be given points in the plane. We want to find the point P = (x, 0) on the x-axis such that the sum of distances PQ + PR is as small as possible. (Before proceeding with this problem, draw a picture!) To solve this problem, we need to minimize the following function of a: f(ac) = over the closed interval a, b where a = and b = We find that f ( ) has only one critical number in the interval at * = where f() has value Since this is smaller than the values of f(@) at the two endpoints, we conclude that this is the minimal sum of distances.Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function 0(3) = 4.5:: + 236253?1 -l- 6750 models their total inventory costs (in dollars) as a function of a: the lot size for each oftheir orders from the supplier. The inventory costs include such things as purchasing, processing, shipping, and storing the equipment. What lot size should Glorious Gadgets order to minimize their total inventory costs? (NOTE: your answer must be the whole number that corresponds to the lowest cost.) What is their minimum total inventory cost? $

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