Question

zander 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. instructions: enter your responses as whole numbers. a. for the given levels of pizza consumption, calculate how many rentals zander can afford with his remaining income. b. using the utility values in the table below, how many pizza slices and how many movie rentals should zander consume each week to maximize his total utility?

Explanation:

Step1: Calculate remaining income for rentals in part a

Let $x$ be the number of pizza slices and $y$ be the number of movie - rentals. The budget constraint is $6x + 3y=24$, or $y = 8 - 2x$.

• When $x = 0$:

$y=8 - 2\times0=8$

• When $x = 1$:

$y=8 - 2\times1 = 6$

• When $x = 2$:

$y=8 - 2\times2=4$

• When $x = 3$:

$y=8 - 2\times3 = 2$

• When $x = 4$:

$y=8 - 2\times4=0$

Step2: Calculate total utility in part b

The total utility $TU$ is the sum of utility from pizza $U_p$ and utility from movie rentals $U_m$. We need to consider the budget - constraint $6x + 3y=24$ (where $x$ is pizza slices and $y$ is movie rentals) and find the combination that maximizes $TU=U_p+U_m$.
We can check all possible non - negative integer combinations that satisfy the budget constraint:

Pizza slices ($x$)	Movie rentals ($y$)	Total Utility ($TU$)
1	6	$20+57 = 77$
2	4	$36 + 54=90$
3	2	$48+50 = 98$
4	0	$58+0=58$

The combination that maximizes total utility is 3 pizza slices and 2 movie rentals.

Answer:

a.

Pizza	Rentals
1	6
2	4
3	2
4	0

b.
Pizza slices to be consumed per week: 3
Movie rentals to be consumed per week: 2