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- A company determines that the demand function for a product can be modeled by p=220-0.02x where x is the number of units produced per week. The fixed cost is $12,000 and the variable cost is $80/unit. Find the number of units that yields the maximum profit.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 first order condition with respect to l?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?
- Suppose a firm is considering investing $20 million in a new marketing campaign. If the price is$65,000/vehicle, they estimate they would sell an additional 2,000 vehicles; If the price is $50,000/vehicle they estimate they would sell an additional 3,000 vehicles. Calculate the company’s profits under both scenarios.A company has determined that its prodor for a product can be described by linear function. The profit from the production and sales of the 150 units is $455, and the profit from 250 units is $895 1. What is the average rate of change of the profit for the product when between 150 and 250 units are sold? 2. Write the equation of the profit function for this product? 3. How many units give break-even for this product?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.
- 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.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.Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a straight commission of $1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month. Write down the month salary payoff table for Jim.
- A firm's total revenues depend on the amount produced (q) according to the function R=240 q-q^(2) Total costs also depend on q:C=q^(2)+60 q+120 a) What level of output should the firm produce in order to maximize profits? What will profits be? b) Show that the second order conditions for a maximum are satisfied at the output level found in part b) Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Marginal revenue of a product is the incremental revenue of selling an additionalunit of that product. Let, the revenue of selling 20 units of a product beRs. 15,000 and the revenue of selling 21 units of the same product beRs. 15,085. Then, the marginal revenue of selling the 21st unit____?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)