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- a.A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packagingtime. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time.The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the ??????? ?????? ?? ?????????'? ????, determine how many of each type of clothing should be made to use all available labour hours?Cindy Jo's Hair Salon is concerned about its rising costs of supplies, energy, and labor, so it is considering investing in better equipment, which hopefully will reduce the time required to perform most hairstyles as well as result in better perceived quality by its customers. It predicts that the added investment will increase output levels as well as reduce energy costs, since some of the new equipment (hair dryers) use less electricity. Inputs and Outputs Hairstyles per week Labor costs per week Energy costs per week Material costs per week Capital investment Using the given information, determine the current and expected single-factor and total productivity measures. Do not round intermediate calculations. Round your answers to three decimal places. Productivity Current (this year) % haircuts/dollar haircuts/dollar haircuts/dollar * haircuts/dollar Expected (next year) X Labor Energy Material Total What is the percentage change in total productivity? Do not round intermediate…1. A company operates plants in both the United States (where capital is relativelycheap and labor is relatively expensive) and Mexico (where labor is relatively cheap andcapital is relatively expensive). b) Under what circumstances will the input choice be relatively similar? 10:10 pm ll
- Q4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.17. For a certain good the production function is given by the equation q = q²qc, where q is the produced output in units of 1000 and qL and qc are the number of units of labour and of capital invested in the production process. Assume that one unit of labour costs 10 units of money and one unit of capital costs 5 units of money. (a) Show on a graph which combinations (qL, qc) generate exactly 64 000 units of output. Put qL on the horizontal axis of the graph and qc on the vertical axis. (b) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units using a budget of exactly 100 units of money. (c) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units in the cheapest possible way.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?
- 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.Price 8 7 6 5 4 3 2 1 110 220 330 440 550 660 Quantity per month 770 880 D -(935, 0.5 990 Tools D₂ 2 S2 с Suppose that in December the demand of mandarin oranges increases by 275 while the supply increases by 110. a) Draw the new curves D2 and S2 in graph above. Plot only the endpoints of the curve above and position those points on the edges of the graphing area.Maximize the following equation: w (x, y) = -3x² + 30x – 6y² + 48y Subject to x + y = 5 O x=2.33; y=2.67 O x=3.33; y=2.67 O x=2.33; y=3.67 O x=12.33; y=12.67
- The profit from the supply of a certain commodity is modeled as P(q) = 71ge-0.29 dollars where q is the number of units produced. 0 ≤ q ≤ 100 (a) Write an expression for the rate of change of profit. (Be sure to use q as the independent variable.) P'(q) dollars per unit (b) At what production level in the domain 0 ≤ q ≤ 100 is the rate of change of profit zero? (Round your answer to the nearest whole number.) q= units (c) What is profit at the production level found in part (b)? (Round your answer to two decimal places.)Definition of economic costs Edison lives in Detroit and runs a business that sells guitars. In an average year, he receives $793,000 from selling guitars. Of this sales revenue, he must pay the manufacturer a wholesale cost of $430,000; he also pays wages and utility bills totaling $301,000. He owns his showroom; if he chooses to rent it out, he will receive $15,000 in rent per year. Assume that the value of this showroom does not depreciate over the year. Also, if Edison does not operate this guitar business, he can work as a financial advisor, receive an annual salary of $50,000 with no additional monetary costs, and rent out his showroom at the $15,000 per year rate. No other costs are incurred in running this guitar business.NOTES: Please explain the given answer and show all the steps. Do not copy from other solutions. Thank you.