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- A company finds that it can sell out a certain product that it produces, at the rate of Tk. 2 per unit. 1 It estimates the cost function of the product to be Tk. 1000 + 2 50 for q units produced. (i) Find the expression for the total profit, if q units are produced and sold. (ii) Find the number of units produced that will maximize profit. (iii)What is the amount of this maximum profit? (iv) What would be the profit if 6000 units were produced?e) i) Given the following Y = C +1 C = 25 + 0.080Yd I = 55 G = 40 T = 10 + 0.10Y Find Y,C, and T.The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $580 per person per day if exactly 20 people sign up for the cruise. However, if more than 20 people (up to the maximum capacity of 90) sign up for the cruise, then each fare is reduced by $4 per day for each additional passenger. Assume at least 20 people sign up for the cruise, and let x denote the number of passengers above 20. (a) Find a function R giving the revenue per day realized from the charter. R(x) = %D (b) What is the revenue per day if 42 people sign up for the cruise? $ (c) What is the revenue per day if 66 people sign up for the cruise? $ Need Help? Read It
- Only 3.2(2) A study indicates that spending money on pollution control is effective up to a point but eventually becomes wasteful. Suppose it is known that when x million dollars is spent on 100-F 0.03x² +9 controlling pollution, the percentage of pollution removed is given by P(x)= (i) At what rate is the percentage of pollution removal P(x) changing when 16 million dollars is spent? Is the percentage increasing or decreasing at this level of expenditure?= 2. The cost of operating a jet-powered commercial (passenger- carrying) airplane varies as the three-halves (3/2) power of its velocity; specifically, Co kny3/2, where n is the trip length in miles, k is a constant of proportionality, and vis velocity in miles per hour. It is known that at 400 miles per hour, the average cost of operation is $300 per mile. The company that owns the aircraft wants to minimize the cost of operation, but that cost must be balanced against the cost of the passengers' time (CC), which has been set at $300,000 per hour. At what velocity should the trip be planned to minimize the total cost, which is the sum of the cost of operating the airplane and the cost of passengers' time?
- It is known that a certain company sells each kg of the product it manufactures at $80, it is also known that the total manufacturing cost "CT" is given by the function CT=(1/1000)x2 +100 , where "x" are the kg of product produced. a) How many units of "x" must the company sell to break even? Value = 100 points.b) How many units of "x" is the optimal quantity that should be sold to optimize the producer's profit? Value = 100 points.c) How many monetary units does that optimal profit for producers amount to? (remember, you will have to prove it mathematically either by the method of the first or by the method of the second derivative). Value = 100 points.How to get the correct answer 0.7271 from the following problem?Find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. 3 f(x) = x° - 27x - 5 (A) f'(x) =
- You manufacture ceramic lawn ornaments. After several months your accountant tells you that your profit P(n) can be modeled by the function P(n)= -0.002n^2+5.2n-1208 where n is number of ornaments sold each month. A) How many ornaments must you make and sell to break even. B) How many ornaments must you make and sell to maximize profit. C) What is the maximum profit. D) How many ornaments must you make and sell in order to earn a profit of $1657.Select the correct answer(s) for each item. If NONE or MORE THAN ONE of the choices is the correct answer, choose E.A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $