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Optimization Methods
Profit Equation
Profit =
Revenue – (Fixed cost + Variable cost)
Profit =
(Selling price per unit)(number of units sold) – [Fixed cost +
(Variable costs per unit)(Number of units sold)]
sX – [f + vX]
sX – f – vX
Profit =
Profit =
s = selling price per unit
f = fixed cost
v = variable cost per unit
X = number of units sold
break-even point equation
0 = sX – f – vX,
0 = (s – v)X – f
Solving for X, we have
f = (s – v)X
X= ____________
Fixed cost
(Selling price per unit) – (Variable cost per unit)
Example 1
If the fixed cost = 350
selling price per unit 15
variable cost per unit 8
Unit of the sell 20
How much the value Profit?
What is the value of break even point?
Problem 1
The Barclay Brothers company is a large manufacturer of adult parlor
games. Its marketing vice president, Rudy Barclay, must make the
decision whether to introduce a new game called Strategy into the
competitive market. Naturally, the company is concerned with
costs, potential demand, and profit it can expect to make if it markets
Strategy. Rudy identifies the following relevant costs:
fixed cost (f ) = $36,000 (costs that do not vary with volume produced,
such as new equipment, insurance, rent, and so on)
variable cost (v) per (costs that are proportional to the number of
games game produced = $4 produced, such as materials and labor)
The selling price(s) per unit is set at $10.
What is the value of break-even point?
Problem 2
• Ray Bond sells handcrafted yard decorations
at county fairs. The variable cost to make
these is 20 $ each, and he sells them for 50 $.
The cost to rent a booth at the fair is 150 $ per
unit. How many of these must Ray sell to
break even?

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