In economics, functions that involve revenue, cost, and profit are used. For example, suppose that R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new grocery cart for a wholesaler. Then the difference P(x) = R(x) - C(x) represents the total profit for producing x carts. Given R(x) = 58x-0.3x² and C(x) = 5x + 15, find each of the following a) P(x) b) R(80), C(80), and P(80) c) Using a graphing calculator, graph the three functions in the viewing window [0, 210, 0, 3200]. a) P(x) = (Simplify your answer. Use integers or decimals for any numbers in the expression.) REED Clear all Check answer

If R(x) represents the company's revenue when selling x items and C(x) represents the company's cost when producing x items. If R(x) = 2x2 - 60x and C(x) = 8050 - 420x, Find the company's profit function (P(x))  Evaluate P(x) when x = 200

A cardboard box manufacturer has decided to introduce a new and improved cardboard box. The set up cost for the production of this new line is $16,600 and the variable costs are $64 per ten thousand cardboard boxes. The company expects to sell ten thousand cardboard boxes for $151. Find a function  P( x) for the total profit from the production and sale of  x (in ten thousands) cardboard boxes.     P(x) = 151x + 16600     P(x) =151x - 16600     P(x) = 87x + 16600     P(x) = 87x - 16600

If ​f(x)=2xand ​g(x)=9x−1​, find​ (fg)(x).   For each pair of​ functions, find​ (fg)(x). f(x)=4x−5​,​g(x)=16x2+20x+25     Let ​f(x)=x2−9​, and ​g(x)=5x. Find the following product function. ​(fg)(x)

A contractor wants to rent a wood chipper from Acme Rental for a day for $150 plus $11 per hour or from Bell Rental for a day for $172 plus $9 per hour. Find a cost function in dollars for using each rental firm. (Let x be the number of hours for which the wood chipper is rented.) Acme   C(x) =        Bell   C(x) =        (a) Find the number of hours for which each cost function will give the same cost. ____hours

A(x) is a quoadratic function. B(x) is a quadratic function. What type of polynomial function is A(x) ·B(x)? 1. 2. A(x) is a linear function. B(x) is a linear function. What type of polynomial function is A(x) · B(x)?

Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced TCD(X) = X² X + 3 where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given by TCH(Y) y² + 2Y + 9 where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 5,000 gloves per week at the lowest possible cost. (a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. min s.t. = X, Y Z 0 = 5 (b) Use Excel Solver or LINGO to find the solution to your mathematical model to determine the optimal…