# Thread: Break Even + equilibrium questions

1. ## Break Even + equilibrium questions

3 somewhat similar questions:

A manufacturer has monthly fixed costs of 112000 dollars and a production cost of 11 dollars for each unit produced. The product sells for 21 dollars per unit.
i) The cost function is C(x) = ___________
ii) The revenue function is R (x) = _________
iii) The profit function is P(x) = ___________
iv) Compute the profit (loss) corresponding to a production level of 5780 units: ______ dollars
v) Compute the profit (loss) corresponding to a production level of 14800 units: ________ dollars

Break - even

A company produces a consumer level scanner at a price of 57 dollars per unit and sells it for 64 dollars per unit. The monthly fxed costs inccured by the company are 27097 dollars.
Compute the break even quantity: _________ units
Compute the break-even revenue: ________ dollers per month.
What should be the level in sales in order for the company to realize a 5% profit over the cost of producing the scanners? ______ units. (round your anwser to the nearest integer)

Market equilibrium

The quantity demanded per month of a certain CD burner is 880 when the price is 138 dollars. The quantity demanded per month is 715 when the price is 153 dollars. The suppliers will not market any CD burners when the price is 50 dollars or less. At a unit price of 53 dollars they are willing to make available only 30 units in the market. Under the assumptions that both supply and demand are linear.
i) Find the demand equation: y= ___________
ii) Find the supply equation: y= ___________
iii) Find the Equilibrium price: ______________ dollars
iv) Find the equilibrium quantity: _____________ units

2. Originally Posted by B-lap
3 somewhat similar questions:

A manufacturer has monthly fixed costs of 112000 dollars and a production cost of 11 dollars for each unit produced. The product sells for 21 dollars per unit.
i) The cost function is C(x) = ___________
ii) The revenue function is R (x) = _________
iii) The profit function is P(x) = ___________
iv) Compute the profit (loss) corresponding to a production level of 5780 units: ______ dollars
v) Compute the profit (loss) corresponding to a production level of 14800 units: ________ dollars
i) You have
- total fixed costs function $\displaystyle FC(x)=112'000$;
- total variable costs function $\displaystyle VC(x)=11x$.

Consequently, you get $\displaystyle C(x) =FC(x)+VC(x)=112'000+11x$.

ii) The revenue function is $\displaystyle R(x)=21x$.

iii) The profit function is $\displaystyle P(x)=R(x)-C(x)=21-(112'000+11x)=10x-112'000$.

iv) Compute the profit (loss) corresponding to a production level of $\displaystyle 5'780$ units:

$\displaystyle \quad P(5'780)=10 \cdot 5'780 - 112'000 = 57'780-112'000 =-54'220$ dollars (ie loss).

v) Compute the profit (loss) corresponding to a production level of $\displaystyle 14'800$ units:

$\displaystyle \quad P(14'800)=10 \cdot 14'800 - 112'000 = 148'000-112'000 =36'000$ dollars (ie profit).

3. Originally Posted by B-lap
3 somewhat similar questions:

Break - even

A company produces a consumer level scanner at a price of 57 dollars per unit and sells it for 64 dollars per unit. The monthly fxed costs inccured by the company are 27097 dollars.
Compute the break even quantity: _________ units
Compute the break-even revenue: ________ dollers per month.
What should be the level in sales in order for the company to realize a 5% profit over the cost of producing the scanners? ______ units. (round your anwser to the nearest integer)

1. $\displaystyle BEQ=\frac{TFC}{P-VC}$, where

- $\displaystyle TFC$ is a total fixed costs;
- $\displaystyle VC$ is a variable costs per unit;
- $\displaystyle P$ is a sell price per unit.

Compute the break even quantity: $\displaystyle BEQ=\frac{27'097}{64-57}= \frac{27'097}{7}=3'871$ units (per month).

2. Compute the break-even revenue: $\displaystyle BEQ \cdot P=3'871 \cdot 64=247'744$ dollars (per month).

3. What should be the level in sales in order for the company to realize a 5% profit over the cost of producing the scanners? 6'856 units. (round your anwser to the nearest integer)

Solution:
Let $\displaystyle x$ - the level in sales (units) in order for the company to realize a $\displaystyle 5\%$ profit over the cost of producing the scanners, then, by the condition of your task, you let

$\displaystyle P \cdot x - (TFC + VC \cdot x) = 0.05 \cdot (TFC + VC \cdot x)$

$\displaystyle P \cdot x - 1.05 \cdot VC \cdot x = 1.05 \cdot TFC$;

$\displaystyle x = \frac{1.05 \cdot TFC}{P - 1.05 \cdot VC} =\frac{TFC}{\frac{P}{1.05}-VC}=\frac{27'097}{\frac{64}{1.05}-57}=\frac{569'037}{83} \approx 6'856$ units.