Find two positive numbers whose sum is 150 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) First Second Number Product, P Number, x 30 150 - 30 30(150 - 30) 3,600 40 150-40 40(150 - 40) = 4,400 50 150 - 50 50(150 - 50) - 60 150 - 60 60(150 - 60) - 70 150 - 70 70(150 - 70) - 80 150 - 80 80(150 - 80) = (b) Write the product Pas a function of x. P) - (c) Use caiculus to find the critical number of the function in part (b). Then find the two numbers. (Enter your answers as a comma-separated list.) (d) Use a graphing utility to graph the function in part (b) and verify the solution from the graph. TO00 se 140 120 so0 100 4000 2000 5540 1000 140 160 1000 6400 -1000 60 100 120 140 160 The solution appears to be at x-