Question 2: a) A manufacture of truck producer needs 4 truck tires (x) for 1 frame (y). The demand function for t is X=126 - 0.5Px and the demand function for f is y=120-py. The total cost of the firm is: TC=2x² + 2xy + 2y² + 380 . Use the Lagrange Multiplier method of constrained optimization optimize the profit, and find all the optimal values. c) Define shadow price and the effect on shadow price in optimization using this context of question 12.
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- Suppose that the profit from the sale of Kisses and Kreams is given by the following, where x is the number of pounds of Kisses and y is the number of pounds of Kreams. P(x, y) = 10x + 6.6y - 0.001x² -0.025y² dollars You know from previous experience that, for such a profit function, profit will be maximized at the critical point of P(x,y). (a) Determine the amounts of Kisses and Kreams that will maximize profit. pounds of Kisses pounds of Kreams (b) What is the maximum profit? (Round your answer to two decimal places.) $Let's say jacky has a demand function for a product made in Ney york city given that the function D(q)=-1.15q+270, where q is the number of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Say that the fixed costs of production for the item is $5,000 and variable costs are $10 per item produced. If 100 items are produced and sold, what are the finds :The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. Graph the profit function, M(x)=550x-3x²-8000, and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): number of sales:
- 2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changingyou are an accountant for a manufacterer of radios. the demand function for the tablets is p= 40-4x2 where x is the number of tablets produced in millions. it costs the company $15 to make a tablet. write an equation for the manufactures profit as a function of the number of tablets produced. the company currently produces 1 million tablets and makes a profit of $21000000, but you would like to scale up production a bit, what greater number of tablets could the company produce to yield the same profitQ2)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 total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 28x + 20,160 and R(x) = 200x - 0.2x2 for 0sxs 1000. Find the value of x where the graph of R(x) has a horizontal tangent line. Find the profit function P(x). Find the value of x where the graph of P(x) has a horizontal tangent line. Graph C(x), R(x), and P(x) on the same coordinate system for 0 sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x).A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³ -0.3x² +600x-800. Currently the company builds and sells 7 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 6 laptops weekly? c) What is the marginal profit when x = 7? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 8 laptops weekly a) The current weekly profit is $ (Round to the nearest cent as needed) b) The decrease in profit is $ (Round to the nearest cent as needed.) c) The marginal profit when x=7 is $ (Round to the nearest cent as needed) CLOT d) The profit resulting from the production and sale of 8 laptops weekly is approximately $ (Round to the nearest cent as needed)A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit function
- 11.2 The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 3,000x + 0.01x2. (a) Find the marginal cost function C'(x). HINT [See Example 1.] C'(x) = Use it to estimate how fast the cost is increasing when x = 4. thousand dollars per television commercialCompare this with the exact cost of airing the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ . Thus, there is a difference of $ . (b) Find the average cost function C, and evaluate C(4). HINT [See Example 2.] C(x) = C(4) = thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudyA small company manufactures and sells fishing poles. The cost of manufacturing fishing poles can be modelled by the function c(x) = 7x + 3, where x is the number of batches (each containing 1000 poles) manufactured. Revenue is modelled by r(x) = x³ - 10x² + 20x. The company has enough workers to produce a maximum of 1200 fishing poles. a State the domain of both the cost and revenue functions. b Find the number of fishing poles that the company should manufacture in order to maximize its profits. The company introduces a new process which allows them to produce 6000 poles. c Find the number of poles that would cause the company to minimize profits (or maximizes losses). d By graphing the cost and revenue functions, find the number of poles which should be manufactured if the company is to just break even (that is, the production level at which the costs and revenues are equal). e It would not maximize the company's profits to produce as many poles as workers are capable of producing.…