A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey andincurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose thatthe cost incurred is given byc(N) = a+bN,for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assumethroughout that the number of drivers N can be any real number (rather than an integer). Each driveruses the road at most once.(ii) Show that the number of drivers that join the road isV - aNe =

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Answered: A particular road is used by N drivers…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a solid soap is 10 cents per soap and 20 cents for the liquid soap. The company developed a model that predicts how many units x1 (of the solid soap), and x2 (of the liquid soap) they will sell per month. According to the model, the amount of units sold depends on the prices p1,p2 (in dollars) of solid and liquid soap through the equation (EQUATION IS ATTACHED) Find the total profit if the price of the solid soap is $1 and the price of the liquid soap is $2.
A company has $10,390 available per month for advertising. Newspaper ads cost $190 each and can't run more than 24 times per month. Radio ads cost $550 each and can't run more than 35 times per month at this price. Each newspaper ad reaches 5750 potential customers, and each radio ad reaches 7250 potential customers. The company wants to maximize the number of ad exposures to potential customers. Use n for number of Newspaper advertisements and r for number of Radio advertisements . Maximize P = subject to < 24 < 35 < $10, 390 Enter the solution below. If needed, round ads to 1 decimal palace and group exposure to the nearest whole person. Number of Newspaper ads to run is Number of Radio ads to run is Maximum target group exposure is рeople
Suppose that a company that makes and sells hand-crafted artwork has a cost function C(x) = 24x + 300, where x is the number of items made, and a revenue function R(x) = 95x, where x is the number of items sold. What is the profit from the 25th item made and sold? There is a $ sign listed next to the answer box, so do not type a $ sign in your answer.
A company has $12,890 available per month for advertising. Newspaper ads cost $190 each and can't run more than 22 times per month. Radio ads cost $590 each and can't run more than 30 times per month at this price. Each newspaper ad reaches 5950 potential customers, and each radio ad reaches 7400 potential customers. The company wants to maximize the number of ad exposures to potential customers. Use n for number of Newspaper advertisements and r for number of Radio advertisements . Maximize P = subject to < 22 < 30 < $12, 890 Enter the solution below. If needed, round ads to 1 decimal palace and group exposure to the nearest whole person. Number of Newspaper ads to run is Number of Radio ads to run is Maximum target group exposure is рeople
A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a solid soap is 10 cents per soap and 20 cents for the liquid soap. The company developed a model that predicts how many units x1 (of the solid soap), and x2 (of the liquid soap) they will sell per month. According to the model, the amount of units sold depends on the prices p1,p2 (in dollars) of solid and liquid soap through the equations ( see attached for equation) Set up a function to describe how the total profit (revenue - costs) depends on the unit prices p1 and p2.
A grocery store sells two brands of a product, the "house" brand and a "name" brand. The manager estimates that if she sells the "house" brand for x dollars and the "name" brand for y dollars, she will be able to sell 63 – 10x + 21y units of the "house" brand and 40 + 13x – 10y units of the "name" brand. Step 1 of 2: Find the revenue function R(x, y).
A sample of 25 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x1), the number of meals eaten outside (x2), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. Coefficients Standard Error Intercept 450.08 53.6 x1 49.92 9.6 x2 10.12 2.2 x3 -.60 12.0 ANOVA df SS MS Regression 3078.39 1026.13 Residual (Error) 2013.90 95.90 Total What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)? Test whether or not there is a significant relationship between the monthly expenditure…
2. A company has identified that the revenue for a particular product is given by the equation R = -x³ + 300x² + 37500x, where x is the number of units sold. How many units need to be sold to obtain the maximum revenue?
From the data given compute the sales price for each product T and O. From the data given compute variable cost per unit for each product T and O. Letter Co. produces and sells two products, T and O. It manufactures these products in separate factories and markets them through different channels. They have no shared costs. This year, the company sold 50,000 units of each product. Sales and costs for each product follow.
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day. 0 Graph the system of inequalities, remember to include x >0 and y > 0 in your graph to get full credit. You will need to include four lines. 25 24 VI
A company has $11,270 available per month for advertising. Newspaper ads cost $180 each and can't run more than 21 times per month. Radio ads cost $570 each and can't run more than 34 times per month at this price. Each newspaper ad reaches 7200 potential customers, and each radio ad reaches 7800 potential customers. The company wants to maximize the number of ad exposures to potential customers. Use n for number of Newspaper advertisements and r for number of Radio advertisements. subject to Maximize P - 21 <34 <$11, 270 Enter the solution below. If needed, round ads to 1 decimal palace and group exposure to the nearest whole person. Number of Newspaper ads to run is Number of Radio ads to run is Maximum target group exposure is people

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