Question

Suppose you get cast on the next season of Project Runway and you are about to begin your first design challenge. Tim Gunn gives you a budget of m = $40 to spend on yards of fabric (x) and spools of thread (y) at Mood (fabric store). The price of a yard of fabric is px and the price of a spool of thread is py.

(a) For the particular Project Runway episode, you must only buy fabrics and thread that cost px = $8 and py = $4, respectively. Graph your budget constraint and be sure to show your calculations. (4 points)

(b) Tim Gunn decides to make a twist! You still must only buy fabrics and thread that costpx = $8 and py = $4, but now Tim is giving you $20 worth of thread for free. Graph your budget constraint and be sure to show your calculations. (5 points)

(c) You have made it past the first round of elimination. Now you are back at Mood shopping for fabric and thread for the next challenge. Today, Mood is having a sale on fabric! The price of a spool of thread is still py = $4. The first 3 yards of fabric is $8 per yard, but then each yard purchased after that costs $2 per yard. Graph your budget constraint and be sure to show your calculations. (5 points)

Answer 1

a)

Given maximum spending amount =m=40

Let quantity of thread=y spools

Quantity of fabric=x yards

Price of thread=py=$4 per spool

Price of fabric=px=$8 per spool

Budget line is given by

m=xpx+ypy

40=8x+4y

We can determine some possible combinations to draw the budget line

Maximum purchase of x=40/8=5 yards

Maximum purchase of y=40/4=10 spools

b)

In earlier case, Budget line is given by

m=xpx+ypy

40=8x+4y

Free quantity of threads=20/4=5 spools

y will be replaced by (y-5) for y>5.

40=8x+4*(y-5) for y>5

40=8x or x=5 for

Following table can be made for possible combinations of x and y

x	y
5.0	0.0
5.0	1.0
5.0	2.0
5.0	3.0
5.0	4.0
5.0	5.0
4.5	6.0
4.0	7.0
3.5	8.0
3.0	9.0
2.5	10.0
2.0	11.0
1.5	12.0
1.0	13.0
0.5	14.0
0.0	15.0

c)

In earlier case, Budget line is given by

m=xpx+ypy

40=8x+4y for

40=2x+4 for

Following table can be made for possible combinations of x and y

x	y
0.0	10.0
1.0	8.0
2.0	6.0
3.0	4.0
4.0	8.0
5.0	7.5
6.0	7.0
7.0	6.5
8.0	6.0
9.0	5.5
10.0	5.0
11.0	4.5
12.0	4.0
13.0	3.5
14.0	3.0
15.0	2.5
16.0	2.0
17.0	1.5
18.0	1.0
19.0	0.5
20.0	0.0