To maximise profits, a competitive firm has a cost function, C(q) = 4q2 + 95 and produces 33 units in order to maximise profits. Although the price of output does not change, the firm decides to build a second factory with the cost function C(q) = 7q2 + 45. To maximise its profits, how many units should it produce in the second factory?
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To maximise profits, a competitive firm has a cost function, C(q) = 4q2 + 95 and produces 33 units in order to maximise profits. Although the price of output does not change, the firm decides to build a second factory with the cost function C(q) = 7q2 + 45. To maximise its profits, how many units should it produce in the second factory?
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- The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x2. (a) Find the marginal cost function C'(x). C'(x) = (b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of x dollars per teddy bear In other words, the cost to produce the 101st teddy bear is approximately dollars (c) Find the average cost function C, and evaluate C(100). C(x) = C(100) = So when they produce 100 teddy bears, the average cost per teddy bear is x dollars. (d) Fill in the blanks: Since the marginal cost is less than the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to decrease.A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount? please solve asap?A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?
- A firm has a linear demand function for it's product.When the price of the product is sh.20,the quantity demanded is 40 units.When the price increases to sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is giving by: Mc = 40q- 2q^2+2 Fixed cost = 5 million Where q= quantity demanded,Mc = marginal cost(sh.million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at the maximum profitA firm has two different plants. Let the cost at plant 1 be given by c(y1) = 5y2 1 + 100y1, and the cost at plant 2 by c(y2) = 500y2. Suppose the firm wants to produce Q units of total output. a) Write out the total cost for the firm. b) Find the marginal cost of production at each plant. c) What is the total cost minimizing level of output at each plant (as a function of the total output)? d) Suppose a non-MPA student (e.g., an MBA student) incorrectly suggests that the firm produce 21 units using the first plant. How should the firm adjust their production amongst the plants to correct this error.The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula Cx) - 100 + 40x - 0.08. (a) Find the marginal cost function C(x). Cx) = 40 - 0.16x Use it to determine how fast the cost is going up (in s) at a production level of 100 teddy bears $ 24 per teddy bear Compare this with the exact cost of produong the 101" teddy bear (in ). The cost is increasing at a rate of s 24 per teddy bear. The exact cost of producing the 101" teddy bear is s Thus, there is a diference of (b) Find the average cost function C, and evaluate č100) (in s). C100) -s x per teddy bear What does the answer tell you? per teddy bear. The average cost of producing the first hundred teddy bears is s Eter an tuber
- Suppose that the cost of producing q appliances is C(q) = 500 – 4q + q? and the demand function is given by p = 14 – 2 q. The quantity that minimizes the average cost function and the corresponding price are g= 22.36 and p= -30.72 a) Why the corresponding price is negative? explain The maximum profit would be -473 b) Why the maximum profit is minus? explain what happensThe cost function for Acme Laundry is C(q)=50+30q+q2, where q is tons of laundry cleaned. What q should the firm choose so as to maximize its profit if the market price is p?The business venture involves the sale of decorative jewelry cases. It costs the startup $280 to produce 40 jewelry cases a week while it costs $320 to produce 60 decorative cases per week as well. the demand, x, for your product is given as a linear function of price, p, where p(x)=15−0.02x 1.Assume that the total cost C(x),is linearly related to the output x. Find an equation for C(x).Hence, determine the Fixed Cost and Variable Cost for this startup. 2.Form the Revenue and Profit Functions based on the information given. 3.Hence, determine the Break-even points to the nearest whole number and discuss the relationship between the intersection points of the graphs of R(x)and C(x)
- Jack's car repair factory has the Total Cost function: TC(Q)=3.30³-540 + 8 where Q stands for the number of hours of repairs. If the market price for car repair is $100 per hour, what are the optimal hours of repairs that Jack will do (round to 2 decimal places)?Beta Industries manufactures floppy disks that consumers perceive as identical to those produced by numerous other manufacturers. Recently, Beta hired an econometrician to estimate its cost function for producing boxes of one dozen floppy disks. The estimated cost function is C = 20 + 2Q². a. What are the firm's fixed costs? b. What is the firm's marginal cost? Now suppose other firms in the market sell the product at a price of $10 c. How much should this firm charge for the product? d. What is the optimal level of output to maximize profits? e. How much profit will be earned? f. In the long run, should this firm continue to operate or shut down? Why?The market for high-quality matsutake mushrooms is dependent on the weather. If the weather is good, one kilogram matsutake mushroom can be sold for $30. In bad weather it sells for only $20 per kilogram. Matsutake mushrooms produced one week will not be kept until the next week, A small matsutake mushrooms producer has a cost function given by C = 0.5q^2 + 5q + 100 where q is weekly matsutake mushrooms production. Production decisions must be made before the weather (and the price of matsutake mushrooms) is known, but it is known that good weather and bad weather each occur with a probability of O.5. How much matsutake mushrooms should this firm produce if it wishes to maximize the expected value of its profits?