ASSIGNMENT # 1
Total points: 100
Fall 2013
Answer Key
1. Carla’s Costume Company plans to sell Gargamel masks this season. Her estimated total cost, as a function of the number (x) of masks bought and sold, is given by :
44 Points
C = 15 x +1320
(a) If the masks are sold for $30 each, determine Carla’s revenue (R) and profit (P), as functions of x.
R = 30x
2 pts
5 Points
P = R –C
P = 30x –15 x – 1320
P = 15 x – 1320
3 pts
(b) How many masks will Carla have to buy and sell to break-even?
3 pts
7 Points
BE P = 0
15 x – 1320 = 0
x = 88
She should buy and sell 88 masks to break even.
2 pts
2 pts
(c) Find the total cost for part b (in dollars).
C = 15 (88) + 1320
C = 2640
3 pts
5 Points
Her total cost will be $2,640 at breakeven level of sales.
2 pts
(d) Sketch a graph of Carla’s cost, revenue, and profit functions, and identify the break-even point. 1 point for each correct line, and 1 point for indicating BE point,
1 point for labeling and showing some values on each axis
$R
$C
$P
5 Points
R
BE
Point
C
P
Masks
(e) If Carla’s goal is to earn a profit equal to 10% of her revenue, how many masks will she have to sell?
2 pts
P = 0.10 R
10 Points
P = 3x
2 pts
12x=1320
3x = 15x-1320
P = 0.10 (30x)
x =110
2 pts
2 pts
Carla should sell 110 masks to make a profit equal to 10% of her revenue.
2 pts
(f) Find the total profit for part e (in dollars).
P = 15 (110) -1320
P = $330
2 pts
4 Points
Carla’s profit will be $330.
2 pts
(g) If Carla’s goal is to earn a profit of $3 per mask, how many masks will she have to sell?
Profit of $3 per mask
P =3x
2 pts
8 Points
12x=1320
3x = 15x-1320
2 pts
x =110
2 pts
2 pts
Carla should sell 110 masks to make a profit of $3 per mask.
2. Use Excel and Goal Seek to confirm your answer for Problem 1(b) above. Submit a printout of your
Excel worksheet formatted like the one below. Indicate the entries for Set cell, To value, and By changing cell that you used in your Goal Seek window. To get this layout with the gridlines and the row and column labels, select Page Layout, then click on the Print check boxes for Gridlines and
Headings. To check that it looks right before you print, click on Print Preview. If it looks right, then click Print. Attach this printout to your assignment.
10 Points
1
2
3
4
5
6
7
8
9
10
11
A
Carla’s Costume Company
B
Your name and ID#
Selling price per mask
Variable Cost per mask
Fixed Cost
$30
$15
$1320
Number of masks
88
Total Revenue
Total Cost
Total Profit
$2640
$2640
0
3 pts
C
Goal Seek Window
B11
Set cell=
0
To value=
By changing cell=
4 pts
D
B7
3 pts
3. Carla estimates she can sell 100 Gargamel masks, if she charges $25 each. She also estimates that she can sell only 80 masks, if she charges $33 each. Assuming it is linear, determine the demand equation that relates the number (q) of masks Carla expects to sell to the price (p) charged per mask.
10 Points p 1 $ 25 p 2 $ 33
m
q 1 100
q1 q 2
m
80 100
20
2 .5
4 pts
162 . 5
4 pts
q 2 80
q mp b
p 2 p1
q 2 .5 P b
The demand equation is q 2 . 5 p 162 . 5
100
33 25
2 . 5 ( 25 ) b
8
b
2 pts
4. Here are the demand and supply functions for Fran’s Foliage Tour tickets this season, where p is the price per ticket (in dollars) and q is the number of tour tickets Fran expects to sell:
36 Points
q = 2 p - 75
q = -2.5 p + 195
(a) For the two functions above, identify which is the demand function and which is the supply function. 4 Points
q = 2 p - 75
2 pts
is supply function (has positive slope).
q = -2.5 p + 195 is demand function (has negative