A certain country uses a progressive tax system. The amount of tax consists of a linear part proportional to the income and a nonlinear part depending on the income by a power law. The total amount of tax is determined by the formula T(W)=aW+(bW+c)p, where W is the income; p is the exponent, a,b,c are some positive numbers. At what level of income the tax rate will be minimal?

A local car rental company rents out each of its cars on a daily basis, i.e. the car must be returned at the end of the day it is rented. The company has a fixed cost of $300 per day and there is an extra cost (for cleaning, maintenance, etc.) of $40 for each car that is rented out. For each car, the company charges $65 rent for the day. (a)  Define an appropriate variable x, and write down the daily cost function C(x). (b)  Write down the daily revenue function R(x). (c)  Find how many cars must be rented out each day for the company to break even. Find the new rental charge p that would result in a profit of $360 per day for renting out 20 cars each day.

A) Assume that the relationship between price p and demand x is linear. Express p as a function of x and find the domain of this function B) Find the revenue function in terms of x and state it’s domain C) Assume the cost function is linear. Express the cost function in terms of x. C(x) =

At the BMV, suppose that the length of time you must wait before speaking to a customer service representative is linearly related to the number of people who are in line in front of you. If there are 8 people in line in front of you, you will wait 44 minutes, and if there are 14 people in front of you, you will wait 68 minutes. How long will you wait if there are 10 people in front of you?

In 2017 the price of a particular earlier model car was about $15,905 with a depreciation of about $1,231 per year. A student had $500 in 2017 and saves $1,700 each year. a) Let H(t) be the value, in dollars, of the desired car t in years since 2017. Let S(t) be the student's total savings, in dollars, t years since 2017. Find equations of H and S.  b) Set up an equation to predict  when the student will be able to buy the car using cash from his savings. State the answer in terms of the year he can buy the car.  c) Now assume that the student earns intrest on his savings. Is your answer from part (b) an underestimate or overestimate? Explain.

An athlete is planning a diet change for training. Each time he eats meal A he gets 20 grams of protein and 30 grams of carbohydrates. Each meal B provides 20 grams of protein and 50 grams of carbohydrates. Each meal A costs $5 each and each meal B costs $7.5. The athlete needs at least 80 grams of protein and 160 grams of carbohydrates. (A) let x be the number of meal A and y be the number of meal B. write inequalities for this linear programming problem. (B) identify the feasible set (C) Minimize the objective function 5x+7.5y (the total cost)

The cost C (in dollars) of producing x units and the revenue R (in dollars) obtained by selling x units are shown in the figure. y 300 000 R 250 000 200 000 150000 100 000 50 000 X 1000 2000 3000 4000 5000

On Utapau, while riding a boga, General Kenobi dropped his lightsaber 435 feet down onto the platform where Commander Cody was. h(s)=−17s2+435h(s)=-17s2+435, gives the height after ss seconds.a) What type of function would best model this situation? Non-Linear Linear b) Evaluate h(4)h(4) =