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- In a certain company, the income from the sale of x thousand pieces of products is given by I (x) = 9x, while the cost of making the same x products is given by C (x) = x ^ 3-6x ^ 2 + 15x + 1. Assuming that I and C are in thousands of dollars and everything produced is sold, what is the maximum profit the producer can make? Argues using first or second derivative criteria.Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where a and b are positive constants and v is the ship's speed in miles per hour. At what speed (in miles per hour) should the ship be operated between two ports, at a distance D miles apart, to minimize the cost? (Hint: Minimize the cost, not the cost per hour.) V = _______mphA researcher at a textbook manufacturing company finds that the revenue is given byR(x)=5x2−40x.What is the marginal revenue at x=20, and what does it mean?Select the correct answer below:The marginal revenue is $40, which means that revenue increases by $40 for each additional textbook produced.The marginal revenue is $160, which means that revenue is $1,600 when 10 textbooks are produced.The marginal revenue is $160, which means that when 20 textbooks are produced, the revenue increases by $160 for each additional textbook produced.The marginal revenue is $40, which means that revenue is shrinking at the rate of $40 per textbook produced.
- Suppose that a political campaign by Loki estimates that the candidate’s polling percentage yand the amount x (in hundred thousands of pesos) that is spent on television advertising arerelated by y = e^0.3x + (5lnx)^2 while the amount that is spent on social media advertising are related by (x −3)^4 + 3y = x. (a) If P300,000 has been spent on television advertising by Loki’s campaign, determine therate of spending that will increase his polling percentage by 2 percentage points per week. (b) Suppose that Loki’s political adversary, Thor, is slowly ramping up his presence on socialmedia. If Loki’s team plans on spending P400,000 on social media advertising and the rateof spending is at P100,000 per week, at what rate will the polling percentage increase?Find the general solution using Reduction of Order: y''=2lnxHow to Find the quadratic function f(x)= ax2+bx+c that goes through (3,0) and has a local maximum at (0,1)?
- Suppose we have a revenue function given by R(x) = 3x3 - ax, Where a is a constant. What would the value of a need to be to have an average revenue of $10 when x = 5?Suppose a baby food company has determined that its total revenue R for its food is given by R=−x^3+30x^2+900x where R is measured in dollars and x is the number of units (in thousands) produced. What production level will yield a maximum revenue?A production level of________________ thousand units will maximize revenue.Solve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematics
- Suppose we have a revenue function given by R(x)=3x^3−αx, where α is a constant. What would the value of α need to be to have an average revenue of $10 when x=5?14. Minimizing Cost. Designs for #1 Canines has determined that when x hundred portable doghouses are produced, the average cost per dog house is given by C(x) = 0.1x^2 - 4.2x + 72.4, where C(x) is in hundreds of dollars. How many doghouses should be produced in order to minimize the average cost per doghouse?Suppose shop A sells q chocolates for q^2+2q dollars whereas the price per chocolate in shop B is 10 dollars. We say that we ''profit from shop A" if we purchase the same quatity of chocolates from shop A at a relatively cheaper price as compared to shop B. Otherwise, we say that we are at a loss. 1.Prove that we will get a large number of chocolates for a cheaper price in shop B compared to shop A. 2.What is the maximum number of choclates we can purchase from shop A so that we do not lose any money. 3.How many chocolates should we buy from shop A to maximise our profit (compared to shop B)? Thank you so much!