In a manufacturing plant, the cost of producing each unit of a product is modeled by the function C(x) = 2x² + 100x + 10, where x is the number of units produced. The revenue generated from selling each unit is modeled by the function R(x) = 20x-5. Find and interpret the expression for the profit function (P(x)) as a combination of these two functions, and determine the production level at which the company maximizes its profit. [✔✔✔✔]

A family plan  for a cell phone has a monthly price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) in ($) of a family for x additional family members added is C(x)=

A firm sells a product for $80 per unit. Raw material costs are$12,50 per unit, labor costs are $27,50 per unit, and annual fixedcosts are $260,000.a. Determine the profit function P(x), where x equals the numberof units sold.b. How many units would have to be sold to earn an annualprofit of $250,000.

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…