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