Q1. Alice runs a restaurant and needs to purchase bananas and carrots to make her dishes. Suppose the price of bananas isdollars per kg, the price of carrots isdollars per kg, and Alice can spend no more thandollars.

Note: You should think of,, andas strictly positive parameters.

Question1

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A)Select the one correct statement from the following.

Question 1Answer

i.

IfAlice wants to purchasekg of bananas andkg of carrots, then her expenditure will bedollars.

ii.

IfAlice wants to purchasekg of bananas andkg of carrots, then her expenditure will bedollars.

iii.If Alice wants to purchase 1 kg of bananas and 1 kg of carrots, then her expenditure will bedollars.

iv.

IfAlice wants to purchasekg of bananas andkg of carrots, then her expenditure will bedollars.

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Question2

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B)If Alice chooses to buy only bananas, then what is the maximum quantity of bananas she can buy given that she can spend no more thandollars?

Question 2Answer

i.

ii.

iii.

iv.

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Question3

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C) If Alice chooses to buy only carrots, then what is the maximum quantity of carrots she can buy given that she can spend no more thandollars?

Question 3Answer

i.

ii.

iii.

iv.

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Question4

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D)Suppose Alice buyskg of bananas, whereis no more than the maximum quantity of bananas that she can buy. For any such, what is the maximum quantity of carrots -- that she can buy?

Question 4Answer

i.

ii.

iii.

iv.

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We can interpretas a functionthat takes the quantity of bananasas the input, and produces the maximum quantity of carrots Alice can buy as the output. If your answer to part (d) is correct, you will find thatis a linear function. For answering the following two parts, it may be helpful to draw the graph of.

Question5

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E)The graph ofwill be a straight line. What is the absolute value of the slope of this straight line?

Question 5Answer

i.

1

ii.

iii.

iv.

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Question6

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F)Which one of the following is the correct interpretation of the absolute value of the slope of?

Question 6Answer

i.

If Alice wants to buy one more kg of carrots, then how many kg of bananas she will have to give up.

ii.

If Alice wants to buy one more kg of carrots, then how many additional kg of bananas she can buy.

iii.If Alice wants to buy one more kg of bananas, then how many kg of carrots she will have to give up.

iv.

If Alice wants to buy one more kg of bananas, then how many additional kg of carrots she can buy.

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Question7

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G)Which one of the following provides the correct interpretation of the-intercept and-intercept when you draw the straight-line graph of?

Question 7Answer

i.

Theintercept gives the minimum quantity of bananas that Alice can buy, and theintercept gives the minimum quantity of carrots she can buy.

ii.

Theintercept gives the minimum quantity of bananas that Alice can buy, and theintercept gives the maximum quantity of carrots she can buy.

iii.

Theintercept gives the maximum quantity of bananas that Alice can buy, and theintercept gives the minimum quantity of carrots she can buy.

iv.

Theintercept gives the maximum quantity of bananas that Alice can buy, and theintercept gives the maximum quantity of carrots she can buy.

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Let the notationrefer to a purchasing-plan, whereanddenote the quantities of bananas and carrots Alice plans to buy. Note that in this problem the notationis not the interval of numbers larger thanand smaller than.

A purchasing-planis ``feasible" if Alice has enough money to execute the plan, i.e., to be able to actually buykg of bananas andkg of carrots.

Question8

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H)Suppose,, and. Which one of the following is not a feasible purchasing-plan for Alice?

Question 8Answer

i.

(0, 50)

ii.

(20, 20)

iii.(0, 0)

iv.

(40, 40)

v.

(100, 0)

vi.

(20, 40)

vii.

(70, 0)

viii.

(0, 20)

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Question9

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I)Suppose,, and. Which one of the following statements is correct about the purchasing-plan .

Question 9Answer

i.

This is a feasible purchasing-plan, and if Alice executes this purchasing-plan then she will utilize all the money she has.

ii.

This is a feasible purchasing-plan, and if Alice executes this purchasing-plan then she will be left with 10 dollars out of the 100 dollars she has.

iii.

This is an infeasible purchasing-plan, and if Alice wants to execute this purchasing-plan then she will somehow need to find an additional 60 dollars.

iv.

This is an infeasible purchasing-plan, and if Alice wants to execute this purchasing-plan then she will somehow need to find an additional 40 dollars.

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Question10

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J)If the purchasing planis a feasible purchasing-plan, then it must be that

Question 10Answer

i.

ii.

iii.

iv.

v.