Answered: Your family likes to eat fruit, but…

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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Question

Your family likes to eat fruit, but because of budget constraints, you spend only $36.00 each week on fruit. Your two choices are apples and grapes. Apples cost $0.40 per pound, and grapes cost $1.20 per pound.

One way to find a linear formula giving the number of pounds g of grapes that you can buy in terms of a, the number of pounds of apples, is to write the budget constraint as an equation and solve it for g.

(a) If you buy 5 pounds of apples, then, of course, you spend 0.40 ✕ 5 = 2.00 dollars on apples. In general, if you buy a pounds of apples, how much money C do you spend on apples? Your answer should be an expression involving a.
C(a) =

(b) Write an expression involving g to represent how much money C you spend on grapes if you buy g pounds of grapes.
C(g) =

(c) Use your answers to parts (a) and (b) to write an equation expressing the budget constraint of $36 in terms of a and g.
36 =

(d) Solve the equation you found in part (c) for g, and thus find a formula expressing g as a linear function of a.
g =

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