7. If exactly 100 people will sign up for a local flight, the airline will change P 3,000.00 per person. Ifmore people will sign up, then the fare is reduced for everyone by P 250.00 per additional person.What is the revenue R(x) where x is the number of additional people? Identify the domain of thefunction model. (Revenue is equal to the number of items sold times the price they were sold at.)

The given no. Of people is 100 and the charge is 3000 per person. If more than 100 people sign up,…

Answered: 7. If exactly 100 people will sign up…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Let S represent the amount of steel produced (In tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. S = 20L0.30 0.70 In this formula L represents the units of labor Input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 45,000 tons of steel at minimum cost. Min s.t. L, C ≥ 0 $ = 45,000 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the nearest Integer.) at (L, C) =
1
Follow the instructions carefully and show the complete solution.
A store has issued two different coupons for its customers to use. One coupon gives customers $20 off their purchase price, and the other coupon gives customers 30% off of their purchase. The store allows customers to use both coupons and choose which coupon to apply first. For this context, ignore sales tax. Let ff be the function that inputs a cost (in dollars) and outputs the cost after applying the "$20 off" coupon, and let gg be the function that inputs a cost (in dollars) and outputs the cost after applying the "30% off" coupon. A customer purchases an item for $120 and asks the cashier to apply the "$20 off" coupon first, followed by the "30% off" coupon. What is the cost of the item after the two coupons are applied? $ A customer purchases an item for $120 and asks the cashier to apply the "$20 off" coupon first, followed by the "30% off" coupon. Use function notation to represent the cost of the item (in dollars) after the two coupons are applied. A customer…
Getting going in the morning was probably hard for folks on the Overland Trail (just as it may be for you today), so coffee was a highly valued commodity. The Cazneau family starts their journey with a supply of 30 pounds of coffee. When they arrive at Sutter's Fort in California, 188 days later, they have only 3 pounds left. 1. Draw a graph showing the amount of coffee remaining as a function of the time elapsed since the start of the journey. For simplicity, assume the Cazneaus consume coffee at a constant rate. 2. Find the average amount of coffee consumed per day. 3. Develop an equation for the function represented by your graph. Find the slope of your graph. 4. 5. Suppose that at the beginning of their 188-day journey, the Cazneaus are 1600 miles from Sutter's Fort. a. How many miles per day do they travel? For simplicity, assume they travel the same distance each day. b. Of course, as the Cazneaus travel, their distance from Sutter's Fort decreases. Write a formula expressing the…
A company produces very unusual CD's for which the variable cost is $ 11 per CD and the fixed costs are $ 35000. They will sell the CD's for $ 55 each. Let a be the number of CD's produced. Write the total cost C as a function of the number of CD's produced. C = $ Write the total revenue R as a function of the number of CD's produced. R= $ Write the total profit P as a function of the number of CD's produced. P = $ Find the number of CD's which must be produced to break even. The number of CD's which must be produced to break even is
X5. A movie theater has a discount for groups of 15 or more people and determines the price per person according to the formula Price = 8-0.15(n-15), where price is given in dollars and n is the number of people. a. Write the revenue R for the movie theater as a function of n. b. Use the function from part (a) to complete the table. What can you conclude from this table? (b) (- 15 30 40 50 60 800 n R(n) ≥ 15
II. Suppose that the total worldwide sales for a song album are approximated by the function: 250x³ x³ +7 where, S(x) = S(x) is the measured in millions of dollars; and x is the number of months since the album is released A. Use a graphing tool to show the graph of S(x) in the context of the situation. B. Construct a table to show the total number of sales for the first two years since the album's release. C. What will be the album's gross sales in the long run? Support your answer analytically using the concept of limits. D. Based on A, B, and C, discuss the trend of the gross sales of the album. Consider the function (for questions E and F) S(x) = E. What will happen to lim S(x) if k is replaced by any value greater than 7? Any value less than 7? Discuss x →00 how the number k affects the limit of S(x) as x gets very large. Support your answer graphically to show the variation. 250x³ x³ + k F. What will happen to lim S(x) if 250 is replaced by any constant? Support your answer…
A baseball team plays in a large stadium. With a ticket price of $15, the average attendance at recent games has been 20,000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 400. a. Express the number of spectators at a baseball game, N, as a function of the ticket price, x. b. Express the revenue from a baseball game, R, as a function of the ticket price, x.
Part C: A pair of jeans are on sale for 10% off, and the sales tax rate is 8%. 1. Write a function s(p) that gives the sale price of a pair of jeans regularly priced at p dollars. 2. Write a function t(p) that gives the total cost including tax for a regularly priced pair of jeans that cost p dollars. Make sure to write your function in simplest form. 3. You want to buy a pair of jeans that are on sale. Does it matter whether the employee applies the sale discount first or adds on the sales tax first to find the total cost? Use compositions of s(p) and t(p) to support your answer.

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