3. Suppose there is a firm that is producing goods x and goods y. The current revenue for the firm is R(qx, y) = 100qr +25qy while the firm's overall cost is: C(qr, gy) = 40 +0.597 - 29rgy +2.5q At this moment the firm has decided to produce q = 50 and qy = 25. Statement: Based on marginal analysis of the data given, the firm's choice of production is optimal.
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- 13. The marginal profit for the new X-99 pogo stick is P'(x) = -0.1x+ 60 where x is the number of sticks produced and sold. The profit is - $1000 when 50 sticks have been produce and sold. a) Find the profit function. b) What level of production of pogo sticks (x) produces a maximum profit?(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡 三 = 9 ..(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?
- 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)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)(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem з
- Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10 – 0.03Q + 0.00005Q2, TFC = 60. The optimum profit is a. 348 b. -245 c. 1,200 d. -15.2 e. 255 f. None of the above80 60 70 10 MC1 00 60 50 Price and cost (dollars) 40 40 30 20 20 10 0 MC2 Demand 50 100 150 Quantity The demand for dishwashers facing the AllClean Co. is given in the figure above. The firm manufactures dishwashers in two plants. MC1 and MC2 are the marginal cost curves for those two plants. How should the firm allocate total output between the two plants in order to maximize profit? Multiple Choice • 10 to plant 1, 40 to plant 2 . 20 to plant 1, 30 to plant 2 . 40 to plant 1, 40 to plant 2 . 20 to plant 1, 60 to plant 2 20 to plant 1, 50 to plant 2 (Ctrl)A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.
- Suppose the firm achieves total revenue of $1,000 by selling 150 units while facing total costs of $900. If the firm produces and sells 151 units, its total revenue is $1,005, and its total costs are $950. Should the firm produce and sell the extra unit? Group of answer choices yes, since marginal profit is positive yes, since profits are positive no, since marginal profit is negative no, since marginal profit is positive You have recently learned that the company where you work is being sold for $1,000,000. The company's income statement indicates next year's profits of $30,000, which have yet to be paid out as dividends. Assuming the company will remain a "going concern" indefinitely and the interest rate will remain constant at 7%, at what (constant) rate does the owner believe that profits will grow? (Hint: the price the owner was willing to pay is the present value of the firm's future cash flows) Group of answer choices 6% 5% 4% 4.5%1/3 1/3 Assume y = f(x1, x2) = x1 x2 . If the input prices are w₁ and w₂ what is profit maximizing y level of output? What is the profit?5. Rusty Trawler imports oil from Saudi Arabia. His cost function (for purchasing and delivering the oil) is TC = 5000+.1Q² where Q is the number of barrels of oil delivered. He may sell all the oil he can deliver for $60 per barrel (so TR = 60Q). Given these conditions, what are Rusty's maximum possible profits? a) $0 b) $300 c) $2,500 d) $4,000