A firm has found from past experience that its profit in terms of number of units x produced, is given by . TP = -X^3/3 + 729x + 2700 a) Find the value that maximizes the profit. b) Find the maximum profit. c) show that your answer in part (a) has been maximized,
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A firm has found from past experience that its profit in terms of number of units x produced, is given by .
TP = -X^3/3 + 729x + 2700
a) Find the value that maximizes the profit.
b) Find the maximum profit.
c) show that your answer in part (a) has been maximized,
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- After an analysis of a large number of small businesses with two to nine employees, it was determined that, in a certain market sector, the operating costs C, in thousands of dollars, could be modeled by the function(pic#2)...., where p is the number of employees working for the firm. On the other hand, the realized revenue, R, of a firm could be determined as a function of the operating costs C, where R=(pic#1)... R and C are expressed in thousands of dollars. a) Based on the analysis, what would be the operating costs for a business with three employees? b) What would be the revenue for a company with three employees? c) Determine the equation that would model the realized revenue, R, as a function of the number of employees.Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)The function Q = L0.3 + K0.7 is an example of _____ returns to scale of production.
- All of these statements about the production function are true EXCEPT a) the curve features 3 distinct regions: increasing returns to scale, constant returns to scale, and diminishing returns to scale. b)the curve's shape matches and its description of the interaction between the graph's axes represents the law of diminishing returns c) it can be applied to many economic markets d) one variation is used to show the difference between firm and market specific riskThe unit price of a product is given by P(X) = 200 - 0,01X and the total cost function C(x) = 50X + 20.000 How many items should be sold to maximize profit?Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. Therefore, at a production level of 200 cups of ice cream, the revenue generated by the company would be $130 for each additional cup of ice cream produced. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (a) Find the value(s) of x at the break-even points. (b) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.
- 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?A Silicon Valley firm produces an output of microchips denoted by y and has a cost function c(y). Assume that the first and second derivatives of the cost function are strictly positive. Of the chips it produces, a fraction 1 − α are unavoidably defective and cannot be sold. Working chips can be sold at a price p and the microchip market is highly competitive. How will an increase in production quality affect the firm’s profit?The total cost of producing the first q items is given by the formula C(q) = -2q^3 + 60q^2 + 1000 (For example, C(10) gives the cost of the first 10 items.) a.) Find the average cost of producing items 6 through 10 b.) Find the marginal cost when q = 8
- Production Function: q=32n+2nl+16l n is the size of net l is the hours of labor employed Total Cost: C=14+2n2+4l2 The price of fish is $2 per unit of fish What is the maximum profit for the firm?The firm will maximize profits by producing____ units of outputs (Enter your response as an integer.)For a unit demand function p=24-8x where x is the number of units and p is the price in tk,finds tge sales function. If the average cost per unit is Tk,8 find a.The profit function, b.The number of units that maximize that profit function.
