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28 November, 16:41

Tom has a weekly allowance of $24, all of which he spends on pizza and movie rentals, whose prices are $6 per slice and $3 per rental, respectively. We can assume that pizza slices and movie rentals are available only in whole-number amounts.

For the given levels of pizza consumption, calculate how many rentals Tom can afford with his remaining income. Fill out rentals

Pizza Rentals

1

2

3

4

Using the utility values in the table below, how many pizza slices and how many movie rentals should Tom consume each week to maximize his total utility?

Pizza slices per week Utils/week from pizza Movie rentals per week Utils/week from rentals

0 0 0 0

1 20 1 40

2 36 2 46

3 48 3 50

4 58 4 54

5 66 5 56

6 72 6 57

7 76 7 57

8 78 8 57

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Answers (1)
  1. 28 November, 17:26
    0
    Tom can afford 6 rentals and his utility is at maximum level, when he consumes 8 slices of pizza and rents 8 movies per week.

    Explanation:

    For the given utility equation 24$ = 6*slice of pizza + 3*rented movie, where pizza levels are 1,2,3 and 4, we have:

    24 = 6*1 + 3 * x

    x = 6

    24 = 6*2 + 3*x

    x = 4

    24 = 6*3 + 3*x

    x = 2

    24 = 6*4 + 3*x

    x = 0

    His total utility is the sum of given utilities per week, which he has from slices of pizza eaten and movies rented. Therefore he should consume 8 slices of pizza and rent 8 movies per week.
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