1 2 Solve for the general equation for ATC (Q) Suppose that TVC (Q) ATC= ATC= 18 Q 1 2 18 1 ATC= + Q² 2 Q 18 1 ATC= + = Q 2 MC=Q, and at an output level of Q=2, we have that TC (2) = 20.
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- AVC=10-0.03Q + 0.00005Q2TFC=60 What is the MC Function?a. sketch the Graph of y = 2* and y = G). Also describe the application of exponential and 3 logarithmic functions in Business. b. A manufacturer estimates that when q thousand units of a particular commodity are produced each month, the total cost will be C(q) = 0.4q? + 3q + 40 40 thousand dollars, and all q units can be sold at a price of p(q) = 22.2 – 1.2q dollars per unit. 1. Determine the level of production that results in maximum profit. What is the maximum profit? 2. At what level of production is the average cost per unit A(q) = ! C(a) minimized? 3. At what level of production is the average cost equal to the marginal cost C'(q)?Use the functions given below to solve the problem. C(x) represents the cost, in dollars, of x units of a product and R(x) represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even, C(x) = 72,000 + 43x and R(x) = 47x The number of units that must be produced and sold in order to break even is units.
- A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. What is the average rate of change of the profit for this product when between 150 and 250 units are sold? Write the equation of the profit function for this product How many units give break-even for this product?Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).Question 2. Company XYZ produces and sells widgets. Production is done at two separate factories, one in Mississauga and one in Scarborough. An analysis reveals that in the Mississauga location, it costs 1 = 59³+10000 (dollars) 50% to produce q widgets in a month, while in the Scarborough location it costs Cs(q) =q² + 20000 (dollars) СM (9) to produce q widgets in a month. The company needs to fulfill orders for a total of 400 widgets in the month of March 2023. (a) How many widgets should each location be assigned to produce so that the total cost of production is minimized? (b) Due to differences in quality control and shipping costs, company XYZ decides to sell widgets produced at each factory at different price levels: widgets produced in Mississauga are to be sold for $2000 each, and widgets produced in Scarborough for $2800 each. Show that it is most profitable for the company to allocate all production to Scarborough.
- Pepper farming is carried out in a greenhouse. Proceeds from the sale of pepper, R,dollars per square meter is determined by the following function. R = 5T (1-e^-x) where T is the temperature set in the greenhouse (Celsius, C^0)and the amount of fertilizer per square meter (kilogram, kg) the costs are as follows: fertilizer cost per square meter is 20?, heating cost is 0.10^2.According to this information a) type the profit function of the manufacturer,?(?, ?).B) determine the end points of the profit function.c) show which endpoints you specify or which ones give the highest amount of fertilizer with the temperature value that makes the profit.The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x) = 56x – 0.020x? 0sxs 2800 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (Round to one decimal place as needed.) (B) R'(X) = (C) R(1000) = R'(1000) = Interpret these results. Choose the correct answer below. O A. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat. O B. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R(1000) dollars per seat. O c. This means that at a…Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?
- Am I solving correctly? I don’t really remember how to derive the AC equation or graph these values that I have found.Does the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $60,000. The variable cost of recapping a tire is $9. The company charges $25 to recap a tire. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit. Determine the annual break-even volume for the Retread Tire Company operation. Graphically illustrate the break-even point using a one way table that relates volume to profit.