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- (a) The cost of producing 5-gallon water bottles is given by C(q) = 0.005q² + 2q + 1000. If 2000 5-gallon water bottles are produced, find the %3D (i) total cost (ii) average cost (iii) marginal cost (iv) marginal average cost SBx2 -3 (Bx+2 (b) Suppose that f(x) if X 2 Find the value of B so that f(x) is continuous everywhere along the real line. (c) The demand for watches is given by p = 7000 - 2q dollars, and the supply of watches is given by p 0.01q? + 2q + 1000 dollars, %3D where q is the number of watches demanded and supplied when the price per watch is p dollars. Based on the information provided, calculate the equilibrium quantity and the equilibrium price for watches.The variation of the total production cost with the production rate for a process is defined as follows. ALL = 2 000 000 + 4q + 2.5 q1.1 (ECU / year) q [=] kg / year a) Plot the change of total production cost according to the production speed. b) Find the annual fixed and variable costs for the case where the production rate is 2 000 000 kg / year. c) Find the average and interface costs for the same production capacity. d) If the market selling price of the product is 20 ECU/ unit, what should be the minimum production rate in order not to damage the organization?A cost function is given. C(q) = 3600 + 5q-0.02q² + 0.00039³ (a) Find the average cost and marginal cost functions. +5 -0.02q +0.0003q average cost 3600 9 marginal cost 5 -0.04q+0.0009q (b) Use graphs of the functions in part (a) to estimate the production level that minimizes the average cost. (Round your answer to the nearest integer.) 194 ✓ units (c) Use calculus to find the minimum average cost. (Round your answer to two decimal places.) $ 32.41 X (d) Find the minimum value of the marginal cost. (Round your answer to two decimal places.) $ 4.56
- The total cost (in dollars) of manufacturing x auto body frames is C(x) = 40,000 + 300x. (A) Find the average cost per unit if 200 frames are produced. (B) Find the marginal average cost at a production level of 200 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 201 frames are produced. (A) If 200 frames are produced, the average cost is $ per frame.Your friend Claire has been designing her own hoodies and giving them as gifts to friends and family. She has decided to sell them online soon by using a 3rd party website with a service surcharge based on her pricing. Using the information below, what is the relationship between Claire's selling price per hoodie and profit margin? (Please plot a graph dipcting the relationship) Costs ($) Base Hoodie Cost $30 Craft Supplies to design $10 Selling Website Service Charge 5%Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is МС- 4x+ 25, that its marginal revenue is MR%3D 75 - 6х, and that the cost of production of 60 units is $8,880. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level.
- Q.6 To express relationship between the average cost functions, which of the following is true: (a) ATC = AFC - AVC. (b) AVC= AFC + ATC. %3D (c) AFC= ATC + AVC. (d) AFC= ATC – AVC. %3Dmajor league baseball plans to sell special commemorative jerseys for the world series. the suppliers says that costs will be C(x)= 10x2-680x-20,000 dollras dor making x jerseys. MLB plans to sell them for 120 dollars each. how many jerseys must be sold for MLB to make a profit?For 9 units of a product, a manufacturer's cost is C(9) dollars and revenue is R(g) dollars, with C(500) = 7500, R(500) = 9800, MC(500) = 15 and MR(500) = 25 . (a) What is the profit or loss at 4 500 ? The is (b) If production is increased from 500 to 501 units, by approximately how much does profit change? The change in profit is
- Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both gasolines are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both gasolines, the percentage of important ingredients in each type of crude oil differs, as does the cost per gallon. The percentage of ingredients A and B in each type of crude oil and the cost per gallon are shown. Crude Oil Cost Ingredient A Ingredient B 1 $0.10 20% 60% 2 $0.15 50% 30% Each gallon of regular gasoline must contain at least 40% of ingredient A, whereas each gallon of high octane can contain at most 50% of ingredient B. Daily demand for regular and high-octane gasoline is 800,000 and 600,000 gallons, respectively. How many gallons of each type of crude oil should be used in the two gasolines to satisfy daily demand at a minimum cost? Round your answers to the nearest whole number. Round the answers for cost to the nearest…The total cost a power plant ($/megawatts) to produce electricity is Y=12+1.3X+0.24 X2 , where X is in megawatts. The estimated selling price of electricity is (16-0.23X) per megawatts. Find the value of X that maximizes profit. Group of answer choices Less than 10 megawatts Between 10-12 megawatts Between 12-14 megawatts More than 14 megawatts DontThe total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)