A manufacturer produces gizmos at a cost of P5 each. The manufacturer computes that if each gizmo sells for x pesos, (15 – x) gizmos will be sold. What is the manufacturer's profit function T(x)? What price x should the manufacturer charge to maximize profit? (Hint: If the profit function is concave, the maximum point is the point where the slope is zero.)
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- Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S = 100N/(N + 1), where N is the number of ads. If each ad costs $4,900 approximately how many ads should Jiffy-Pol buy in order to maximize its profits? A) 2,853. B) 1428. C)98 D) 477.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.Complete all of the following definitions
- 1.The price p in dollars of a certain commodity and the quantity x sold obey the demand equation p= -1/5 + 200 where 0<=x <=1000. Suppose that the cost C in dollars of producing x units is C= the square root of x divided by 10 + 400. Assuming that all items produced are sold, find the cost of c as a function of the price p. 2. The value V of a vehicle is v(t)= 420,000(0.965)^t. What would be the car's worth in 2 years? In how many years would the car be worth $325,000?If TC = 98 + 15Q + 6Q2 , what is the marginal cost at when Q=7? Enter as a value.Appleway Industries produces apple juice and sells it in a competitive market. The firm’s manager must determine how much juice to produce before he knows what the market (competitive) price will be. Economists estimate that there is a 30 percent chance the market price will be $2 per gallon and a 70 percent chance it will be $1 when the juice hits the market. If the firm’s cost function is C = 200 + 0.0005Q2, how much juice should be produced to maximize expected profits? What are the expected profits of Appleway Industries?
- 10)Given the production function f (L K) = L2 / 3. K1 / 3, where L is the working hours and K is the capital. assuming that the capital price is r = 4 euros and the price per hour of work is w = 27 euros and that all the factors of production are variable, what is the minimum cost of producing 10 units of product? Choose one: A) 260e B) 230e C) 240e D) 250e E) 270eThe cost formula for a company can be modeled by C=1092+40x+0.1x2C=1092+40x+0.1x2 where xx represents the number of items made. A formula for the company's income is modeled with R=108x−0.9x2R=108x-0.9x2, where xx is the number of items sold. A company will break even when its costs equal its income. How many items must a company make and then sell to break even? Answer: (If there are multiple answers, separate the answers with a comma.)Consider the market for a bond which has a face value of $2,000, pays a coupon of $100, and matures in 1 year (that is, you will get the face value and one coupon payment next year). Suppose the orignal demand for such bonds is given by P=4,000-2Q, and that the supply of such bonds is given by P=1,000+Q. Keeping this supply curve fixed, suppose the demand curve next year will be given by P=3,400-2Q. What would be my rate of return if I bought the bond at the equilibrium price today and sold it at the equilibrium price tomorrow? 5% -.05% 10% -5%
- Assume P = 250 - 1Q and TC = 156 + 1Q2. What level of production maximizes profit? Enter as a value (round to two decimal places if necessary).Suppose that there is a civil case against a defendant. The probability of the plaintiff winning is fixed at p=0. 5. The damages are given by V(CP ,CD)=6+6 ln(CP +1)−6 ln(CD +1). Find the optimal legal expenditure es under an American-style legal fee system. For what amount would the defendant agree to settle?The equations that correspond to the following market are as follows: Qd = -200P + 3,000 Qs = 200P - 400 During finals week, Midnight Cookies runs the 'Manager's Special,' which sells the same cookie four-pack for $5. Holding all other variables constant, and assuming that Midnight Cookies changes nothing to their production plans, calculate the deadweight loss generated in the Midnight Cookies market from the store running the Manager's special during finals week. Omit any units and round to the nearest cent.