MGSC 1205
Introduction to Quantitative Methods I
Fall 2010
Assignment #1
9/28/2010
1 of 7
Solution to Assignment #1
Due:
1 pm, Friday, September 24 2010
#
1.
The management of
the Toy R4U
Company needs to decide whether to introduce a certain new novelty toy for the
upcoming Christmas season, after which it would be discounted. The total cost required to setup the production
and market this toy would be $500,000 plus $15 per toy produced. The company would receive revenue of $35 for
each toy sold.
The decision Variable is
x
= number of toys to produce.
Fixed cost
F
= $500,000
Variable cost per unit
c
= $15
Sell price per unit
p
= $35
(a)
Assume that company could sell every unit of this toy produced. Write an expression for the Total Cost (C),
Revenue (R), and Profit (P) functions for the company in terms of
x
, the number of units produced.
The cost function:
The revenue function:
The profit function:
(b)
How many units must be produced and sold in order to break even?
To break even, we have
Therefore, the Toy R4U should make 25,000 toys to break even.
x =
25,000 is called the breakeven point (BEP).
(c)
What is the company
’
s break-even point in dollars (BEP
$
)? That is, how much is the company
’
s total cost,
revenue and profit at the break-even production level?
When breakeven,
x =
25,000. Thus,
Therefore, when
x
= 25,000, the total cost equals the revenue, equals $875,000.
R
=
C
= $875,000 is also called the breakeven point in dollars (
BEP
$
).
(d)
Find the total cost, revenue and profit when 35,000 toys are made and sold.
When x = 35,000
The cost:
The revenue:
The profit:
or
Therefore, when 35,000 toys are made and sold, the total cost would be $1,025,000, the revenue
$1,225,000, and the profit $200,000.
(e)
If the company wants to make a profit of a million dollars, how many units must be made and sold?
We want
:
To make a million dollar profit, the company has to produce and sell 75,000 toys.