Suppose that the first P300,000 income earned is not taxed at all, the next P500,000 earned is taxed at arate of 20%, the next P1,500,000 is taxed at a rate of 30%, and any additional income is taxed at the rateof 40%. Let T(y) represent the income tax schedule.Find and graph the tax function T(y), defined on y 2 0b. Determine the points of non-differentiability for this function and explain why.Find and graph the marginal tax function on y 2 0.а.С.T(y)d. Find and graph the average tax functionon y 2 0.y

“Since you have asked multiple questions, we will solve the first question for you. And as the 2nd…

Answered: Suppose that the first P300,000 income…

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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An electric company charges its customers $0.0577 per kilowatt-hour (kWh) for the first 1000 kWh used, $0.0532 for the next 4000 kWh, and $0.0511 for any kWh over 5000. Find a piecewise-defined function C for a customer’s bill of x kWh.
Suppose Becky gets a sales bonus at her place of work that gives her an extra $400 of disposable income. She chooses to spend $300 and save the remaining $100. From this, you can tell that Becky's marginal propensity to consume (MPC) is0.75 , and her marginal propensity to save (MPS) is0.25 . Mathematically, it must always be true that: Saving = a. Disposable income+Comsumption b. Comsumption-Disposable income c. Disposable income-Consumption Therefore, it must also be true that: MPS = a. 1-MPC b. 1+MPC c. MPC
The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost is $14 per widget (so it costs $14 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.)C = (b) Express using functional notation the total cost if there are 225 widgets produced in a month.C( )Calculate the total cost if there are 225…
A salesperson makes a base salary of $50, 000 a year plus 4% commission on all sales up to (and including) $275, 000 If they exceed $275, 000 in sales for a calendar year, the salesperson's commission jumps to 8% for all their remaining sales over $275, 000 . The salesperson's total salary S for a given year is based on their total sales X . Write the piecewise-defined function S(x). hint: do not forget to include the base salary of $50, 000 when finding the pieces of the function if x 275, 000 .04x+50000 S(x) = { .08x+20000 The submission, .08x+20000, is incorrect.
When a homeowner has a 25-year variable-rate mortgage loan, the monthly payment R is a function of the amount of the loan A and the current interest rate i (as a percent); that is, R = f(A, i). Interpret each of the following. (a) f(150,000, 8) = 773.89 For a loan of $150,000 at 8% interest, the monthly payment is $773.89. For a loan of $150,000 at 7.7389% interest, 800 monthly payments would be required to pay off the loan. For a loan of $150,000 at 8% interest, 773.89 monthly payments would be required to pay off the loan. For a loan of $150,000 at 7.7389% interest, the monthly payment is $800. af (b) (150,000, 8) = 68.74 O For a loan of $150,000 at 8% interest, an 8% change in the interest rate would result in a $68.74 change in the monthly payment. For a loan of $150,000 at 8% interest, a 6.874% change in the interest rate would result in an $8.00 change in the monthly payment. For a loan of $150,000 at 8% interest, a 1% change in the interest rate would result in a $68.74 change…
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =
The following graph shows the approximate value of the United States Consumer Price Index (CPI) from December 2006 through July 2007. On the graph titled "CPI Dec 2006-July 2007," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 202), goes up and right becoming more steep, passes through the approximate point (3.5, 205.5), goes up and right becoming less steep, and ends at the approximate point (7, 208.7). The approximating curve shown on the figure is given by I(t) = −0.04t3 + 0.4t2 + 0.1t + 202 (0 ≤ t ≤ 7), where t is time in months since the start of December 2006. (a) Use the model to estimate the monthly inflation rate in January 2007 (t = 1). Recall that the inflation rate is I′(t) I(t) . (Round your answer to three decimal places.) (b) Was inflation slowing or speeding up in January 2007? slowing downspeeding up (c) When was inflation speeding up? When was inflation…

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