(a) A cruise line offers a trip for $1700 per passenger. If at least 100 passengers sign up, the price is reduced for all the passengers by$10 for every additional passenger (beyond 100) who goes on the trip. The boat can accommodate 250 passengers. What number ofpassengers maximizes the cruise line's total revenue? What price does each passenger pay then?The number of passengers that maximizes the cruise line's total revenue is iThe price the passengers pay is $i(b) The cost to the cruise line for n passengers is 80,000+ 500n What is the maximum profit that the cruise line can make on one trip?How many passengers must sign up for the maximum to be reached and what price will each pay?The maximum profit that the cruise line can make on one trip is $iThe number of passengers that must sign up for the maximum to be reached ismust pay $ i, and each passenger

Let, N be the number of passengers of the cruise.

Answered: (a) A cruise line offers a trip for…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 22E: Making crafts Two artists, Nine and Rob, make yard ornaments. They get 80 for each wooden snowman...

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In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?
Inventories An electronics store manager stocks from 20 to 30 IBM-compatible computers and from 30 to 50 Apple computers. There is room in the store to stock up to 60 computers. The manager receives a commission of 50 on the sale of each IBM-compatible computer and 40 on the sale of each Apple computer. If the manager can sell all of the computers, how many should she stock to maximize her commissions? Find the maximum commission. Inventory IBM Apple Minimum 20 30 Maximum 30 50 Commission 50 40
Making crafts Two artists, Nine and Rob, make yard ornaments. They get 80 for each wooden snowman they make and 64 for each wooden Santa Claus. On average, Nina must work 4 hours and Rob 2 hours to make a snowman. Nina must work 3 hours and Rob 4 hours to make a Santa Claus. If neither wishes to work more than 20 hours per week, how many of each ornament should they make each week to maximize their income? Find the maximum income. Snowman Santa Claus Time Available Robs Time hr 2 4 20 Ninas Time hr 4 3 20 Income 80 64
Investing in BondsA woman wishes to invest 12,000 in three types of bonds: municipal bonds paying 7 interest per year, bank certificates paying 8, and high-risk bonds paying 12. For tax reasons she wants the amount invested in municipal bonds to be at least three times the amount invested in bank certificates. To keep her level of risk manageable, she will invest no more than 2000 in high-risk bonds. How much should she invest in each type of bond to maximize her annual interest yield? Hint: Let x= amount in municipal bonds and y= amount in bank certificates. Then the high-risk bonds will be 12,000xy.
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