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- Find the first, second, and cross partial derivatives for the following function:z=f ( x , y )=12 x4−6 x2y+4 xy3Take the derivatives of the following functions. Do NOT simplify. f(x) = 20x^3 f(x) = 15x + 20x^2 I cannot figure out how the equation goes from q1 = D1 (p1; p2) = S(1/2 + (p2-p1/2t)) to q1 = S/2 +(p2-p1/2t) why is S not in the numerator of both terms? i.e. q1 = S/2 + S(p2-p1/2t)
- Can you show how Qsc is = 2Pc? Which is the answer for this.If Qd= 20-0.5P, find the slope of the function 20 5 1 -0.5Q4 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?
- Rob is considering a new marketing campaign to promote his new widgets. He currently buys his widgets for $40 and sells them for $100. His most recent sales for 2022 were 50,000 widgets. I he campaign is expensive and advertising and other costs of promotion will be $500,000; however, he believes the campaign will increase sales by 10% over his 2022 sales. Rob wonders if this campaign is a good investment and wants to calculate the return on his $500,000 marketing campaign. Using the space below, demonstrate how an ROl calculation could help Rob make the best decision.In the past four years, the annual returns of one company’s stockare 12%, 18%, and –14%, and 7%.a) What is the geometric average return? b) What is the arithmetic average of the returns? c) According to an economist’ forecast on the Year 2020, the probabilities of repeatingthe performances of the former four years are 30%, 30%, 20%, and 20%, respectively.What is the expected return of the stock in the Year 2020Use the function below (whose parameters qualify it as a STC function) to answer the questions. STC = 4850 + 40Q - 1.5Q^2 + .04Q^3 FC = $4,850 AFC = 4,850 / Q (I calculated this) AVC = 40 - 1.5Q + .04Q^2 (I calculated this) MC = 40 - 3Q + 0.12Q^2 (I calculated this)
- Q1. A real-estate investor has the opportunity to purchase a small apartment complex. The apartment complex costs $4 million and is expected to generate net revenue (net after all operating and finance costs) of $60,000 per month. Of course, the revenue could vary because the occupancy rate is uncertain. Considering the uncertainty, the revenue could vary from a low of − $10,000 to a high of $100,000 per month. Assume that the investor’ s objective is to maximize the value of the investment at the end of 10 years.a) Do you think the investor should buy the apartment complex or invest the $4 million in a 10-year certificate of deposit earning 9.5%? Why? b)b) The city council is currently considering an application to rezone a nearby empty parcel of land. The owner of that land wants to build a small electronics-assembly plant. The proposed plant does not really conflict with the city’s overall land use plan, but it may have a substantial long-term negative effect on the value of the…A mutual fund has a rate of return for five years of 10%, 14%, 10%, and 22% . Calculate the geometric mean. Round to the nearest tenth of a percent.A farmer believes there is an equal chance that the next growing season will be abnormallyrainy. His expected return function has the formExpected return = 0.5lnYNR + 0.5lnYRwhere YNR and YR represent the farmer’s income in the states of “normal rain”and “rainy,” respectively.Suppose the farmer must choose between two crops that promise the following incomeprospects:Crop YNR YRMaize $14,000 $5,000Cotton $9,500 $7,500a) Which of the crops will he plant?b) Suppose the farmer can plant half his field with each crop. Would he choose to do so?Explain your result.c) What mix of Maize and Cotton would provide maximum expected utility to this farmer?d) Would Maize crop insurance, available to farmers who grow only Maize, which costs$2,000 and pays off $4,000 in the event of a rainy growing season, cause this farmer tochange what he plants?