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- 3. Instagram has a revenue function of R(q) = 5q2² - 10q + 600 and a cost function of C(q) = 3q² + 200, where R(q) and C(q) are measured in thousands of dollars and q represent the number of companies who advertise on their platform measured in hundreds. Instagram has a capacity to advertise for 10000 companies in any given month on its platform. a) How much will Instagram's marginal cost be for advertising at 74% of its P capacity? b) Calculate and interpret Instagram's marginal revenue when 8000 companies advertise with them. c) How many companies must advertise with Instagram so that its maximum profit can be achieved? d) Calculate Instagram's maximum revenue at/for the number of companies needed to maximize its total profit? IA manufacturing process has a total cost function given by the equation C = 10 + 4x and a total revenue function given by the equation R = 22x - 4x2 where x is the quantity produced in ’00 units and C and R , are both N$’00. i. Using the cost equation, C = 10 + 4x, identify the value of the company’s fixedcosts (i.e. those that remain constant irrespective of the quantity produced) andvariable costs (i.e. those that vary according to production) for thismanufacturing process. ii. Construct a table to calculate the value of C and R using the values 0, 1, 2, 3, 4and 5 for x. iii. (Using the data from the table in (ii), plot a fully labelled graph for C and Ragainst x. Use the graph drawn in (iii) to determine:iv. The quantity of units produced where the manufacturing process breaks even(i.e. where neither a profit nor a loss is made). v. The range of x in which the manufacturing process makes a profit and the rangein which the manufacturing process makes a loss. vi. The profit or loss…5. Solve IVP у" - 4y" + 7y - бу %3D 0, у(0) %3D 1, у'(0) — 0, у" (0) — 0
- 3. (VP-1) Use the method of variation of parameters to find the general solution to the following equation: y" - 2y + y = = ex X15. Graphically solve the following: тахітize p %3D 3х + 2у subject to: 0.2x + 0.1y 0A company has determined that the price and the monthly demand of one of its products are related by the equation D = (375-P)^o.5 , where p is the price per unit in dollars and D is the monthly demand. The associated fixed costs are $1,176/month, and the variable costs are $95/unit. What is the optimal number of units that should be produced and sold each month?
- If company A manufactures t-shirts and sells them to retailers for US$9.80 each. It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers. The demand for its product is p = 15 - (x /25) , its production cost per unit is US$5.00 and its fixed cost are the same as for company A. For reference to the questions I need solved see the solutions below. (i) Derive the total revenue function, R(x) for company A. Revenue of Company A = sales of the company Let x be the number of units sold. R (x)A = 9.8x (ii) Derive the total cost function, C(x) for company A Cost of Company A = Fixed Cost + Variable Cost (x)y = 2625 + 2.3x (iii) Derive the profit function, Π(x) for company A. Profit function to compound Π (x)A = Revenue - Cost Π (x)A = 9.82 - (2625 + 2.3x) Π (x)A = 7.5x - 2625 The questions I need solutions for are: (iv) Using a spreadsheet, create a…3) Personal taxes Suppose that the percent of total personal income that is used to pay personal taxes is given by y = 0.034x² – 0.044x + 12.642 where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). (a) Verify that x = 7 is a solution of 14 = 0.034x² – 0.044x + 12.642. (b) Find the year or years when the percent of total per- sonal income used to pay personal taxes is 14.How can I find “m” in y=mx+b equations? That’s the one part I’m struggling with.
- 48. If the complementary function of this equation is ye = cie² +c2xe", then by the method of variation of parameters, we can assume form of its particular solution, y, = u141 + U2Y2 · Determine uj.个|。 4 of 9 + Automatic Zoom >> Problem Set: C 1. Solve the following: > 3 (b) 5t² – 20 (2) Gabrielle is given the choice of two positions, the first paying $6400 per month and the other paying $4000 per month plus a 5% commission on all sales made during the month. What amount of sale must she make a month for the second position to be more profitable? (3) Create the function which best describes the graph show below. f(x) 8 -7 -6A company operates two plants which manufacture the same item and whose total cost functions are C1 = 8+0.03q? and C2 = 5.4 + 0.04q3, where qi and q2 are the quantities produced by each plant. The total quantity demanded, q = q1 + q2 , is related to the price, p, by p = 40 – 0.04q. How much should each plant produce in order to maximize the company's profit? 91 = 92 Adapted from M. Rosser, Basic Mathematics for Economists, p. 318 (New York: Routledge, 1993).
