1. A soft drink vendor at a popular beach resort analyzes his sales records and finds...

 

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1. A soft drink vendor at a popular beach resort analyzes his sales records and finds that if he seels x cans of pop in one day, his profit in dollars is given by the function P(x) = -0.012+3x-80. (a) What is his maximum profit per day? (b) How many cans must he sell to achieve maximum profit? 2. Sketch the graph of f(x) = -2x + 12x + 26 by first completing the square, and then determining the vertex point and x- and y- intercepts. 3. A rectangular box with a volume of 125 cubic inches has a square base. Find a function that models its surface area S in terms of the length x of one side of its base. 4. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river's edge. What are the dimensions of the field of the largest land area that he can fence off? (Hint: Model the problem in one of two ways, either using the length and/or using the width. Then, find the maximum value of the function. Use that to determine the field's dimensions, length and width.) 1. A soft drink vendor at a popular beach resort analyzes his sales records and finds that if he seels x cans of pop in one day, his profit in dollars is given by the function P(x) = -0.012+3x-80. (a) What is his maximum profit per day? (b) How many cans must he sell to achieve maximum profit? 2. Sketch the graph of f(x) = -2x + 12x + 26 by first completing the square, and then determining the vertex point and x- and y- intercepts. 3. A rectangular box with a volume of 125 cubic inches has a square base. Find a function that models its surface area S in terms of the length x of one side of its base. 4. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river's edge. What are the dimensions of the field of the largest land area that he can fence off? (Hint: Model the problem in one of two ways, either using the length and/or using the width. Then, find the maximum value of the function. Use that to determine the field's dimensions, length and width.)