3. Suppose that a firm's profit function is π = 80q₁ - 2q1-9192-3q2 +100q2, where it must be that q₁ +42= 12. Solve for q1, 42, . Solve for X*.
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- 3. Suppose that a firm's profit function is π = 8091 -2q-9192-3q2 + 100q2, where it must be that q₁ +92 = 12. Solve for qi, q2, 7. Solve for A*.1. It costs $25,000 to build 30 refrigerators. It costs $30,000 to build 40 refrigerators. Assuming that the cost function is linear, find the cost function C(x) where x is the number of refrigerators built. If each refrigerator sells for $1500, find the revenue function, profit function, and break-even point.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)
- Exercises 47-50 describe a number of business ventures. For each exercise, a. Write the cost function, C. b. Write the revenue function, R. c. Determine the break-even point. Describe what this means. 47. A company that manufactures small canoes has a fixed cost of $18,000. It costs $20 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.) 48. A company that manufactures bicycles has a fixed cost of $100,000. It costs $100 to produce each bicycle. The selling price is $300 per bike. (In solving this exercise, let x represent the number of bicycles produced and sold.) 49. You invest in a new play. The cost includes an overhead of $30,000, plus production costs of $2500 per performance. A sold-out performance brings in $3125. (In solving this exercise, letxrepresent the number of sold-out performances.) 50. You invested $30,000 and started a business writing greeting cards. Supplies cost 2¢ per card…If the profit function is T = - Q² + 7Q -10 What is the value of the maximum profit Select one: C a. Tmax. = -3.5 b. Tmax. = 2.25 C C. Tmax. =7 d. Tmax. = 3.5Assume that the cost to produce x school T-shirts is given by C(x) 6x+750 and the T-shirts are sold for 521 each. Thus, the resulting revenue function is R(x)=21x a Find the profit function P(x) b. Find the profit or loss from the sale of 10 T-shirts e. How many T-shirts must be sold to break even?
- 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.) $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?A firm has found from past experience that its profit in terms of number of unit X produces is given by –*+ 729x + 2700 Find the value of x that maximizes the profit and the profit per unit of product, when this maximum level is achieved.
- A company produces at most 15 (thousand) widgets per year. Its profit P, in thousands of dollars, is a function of n, the number of widgets prouduced per year( in thousands of widgets) the marginal profit is given by dp/dn = 20 + n -n^2. A. What is the marginal profit if n= 3 ( thousand widgets) should the company increase or decrease production B. What is the marginal profit of n= 8 ( thousand widgets) should the company increase or decrease production C. How many widgets should the compay proudcue in order to maximize1/3 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?(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 ..