A manufacturer can produce at most 90 units of a certain product each year . The demand equation for the product is p= q2-100q+1800 and the manufacturer's average cost function c=2/3q2-55q+12000/q Determine the profit maximizing output q and the corresponding maximum Profit . The profit maximizing output q is 60

The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x)=-2300+40x R(x)=840x-x² a) Determine and simplify the profit function. Write your answer in descending order. P(X)-

A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p=85-0.2D (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,500 per month and the variable cost is $20 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month?

A manufacturer of hospital supplies has a uniform annual demand for 500,000 boxes of bandages. It costs $20 to store one box of bandages for one year and $ 500 to set up the plant for production. How many times a year should the company produce boxes of bandages in order to minimize the total storage and setup costs? The company should produce boxes of bandages □ time(s) a year. A manufacturer of hospital supplies has a uniform annual demand for 500,000 boxes of bandages. It costs $20 to store one box of bandages for one year and $500 to set up the plant for production. How many times a year should the company produce boxes of bandages in order to minimize the total storage and setup costs? C The company should produce boxes of bandages time(s) a year.

(i) If the demand function for a particular commodity is p=−0.09x+51 and the total cost function C(x)=1.32x2+11.7x+101.4,where x is the level of production. Find (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?

Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) 3D0.25x². Their orange juice is demanded only in Muscat (Muscat demand is Xm= 100-2Pm) and Salalah (Salalah demand is 100-4P,). Therefore, the total demand is x-St Xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? Answer

The HAC at Humberview has decided to sell Gatorade to raise money.  The demand function is described by  px=-4x+340 , where x is the number of bottles, in hundreds, and px is in dollars.  The cost function, in dollars, is described by Cx=300x-275.  Determine the number of Gatorade bottles they must sell so that they maximize their profit.

A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. p=600-0.1x and C(x)= 15,000+ 130x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenus? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.) The maximum weekly revenue is S. (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.) The maximum weekly profit is $ (Round to the nearest cent as needed.)

A firm can produce 100 units per week. If its total cost function is C = 400 + 1000x dollars and its total revenue function is R = 1100x – x? dollars, how many units, x, should it produce to maximize its profit? units Find the maximum profit. $

The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2p Develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.