PERTANYAAN

1. A publisher of a current economics textbook determines that the manufacturing costs directly attributable to each book are $55 and that the fixed costs of production are $225,000. The publisher sells each book for $100 per copy.

Determine the equation relating the total cost to the number of books published.
Determine the equation relating the sales revenue to the number of books sold.
Determine the profit if 3000 books are published and sold.
Algebraically determine the BEP for this process.
Determine the BEP in Exercise 1 graphically. Which method do you prefer?

2. A manufacturer of staplers determines that the variable costs directly attributable to each stapler are $2 and that the fixed costs are $15,000. Each stapler sells for $12.00.

Determine the BEP for this process both graphically and algebraically.
Determine : the total cost of the process at the BEP
Determine the total sales revenue of the process at the BEP
Calculate the profit at the BEP

3. A publisher of a current solution manual to a textbook determines that the manufacturing costs directly attributed to each manual are $4 and that the fixed costs are $15,000. The publisher sells each manual for $29.99 per copy.

Determine the equation relating the sales revenue to the number of manuals published.
Determine the equation relating the total cost to the number of manuals.
What will the profit be if 2000 manuals are published?
Using Equation of BEP, determine the BEP for this process.
Determine the BEP Which method do you prefer?

4.AirAsia is evaluating a new regional route. The fixed cost per season (lease, crew base setup, marketing, slot fees) is USD 12,000,000. The variable cost per passenger (fuel, catering, handling, sales fees) is USD 24, while the average fare is USD 59.

Write the sales revenue equation as a function of passengers.
Write the total cost equation as a function of passengers.
What is the profit if the airline carries 420,000 passengers on this route during the season?
Using the BEP formula, determine the break-even number of passengers.
Determine the BEP graphically (plot R and C on the same axes). Which method do you prefer and why?

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BUKTI

1.Publisher (books)

Given: variable cost per book = $55, fixed cost = $225,000, price = $100 per book.

(a) Total cost equation
$C(x)=225{,}000+55x$
(where $x$ = number of books)

(b) Sales revenue equation
$R (x) = 100 x$

(c) Profit if 3,000 books are published and sold
Profit $P(x)=R(x)-C(x)=100x-(225{,}000+55x)=45x-225{,}000$ .
For $x=3{,}000$ : $P(3000)=45(3000)-225{,}000=135{,}000-225{,}000=-90{,}000$ .
So a loss of $90,000.

(d) Algebraic BEP (break-even point)
Set $R (x) = C (x)$ : $\Rightarrow 45x=225{,}000 \Rightarrow x=\dfrac{225{,}000}{45}=5{,}000.$
So BEP = 5,000 books.

(e) Graphical BEP and preference
Graphically you would plot $R (x) = 100 x$ and $C(x)=225{,}000+55x$ and find their intersection at $x=5{,}000$ .
Preference: I prefer the algebraic method for exact BEP values (fast and precise). The graphical method is useful for intuition and visualizing margins, but algebra gives the exact number.

2.Staplers manufacturer

Given: variable cost per stapler = $2, fixed cost = $15,000, price = $12 per stapler.

(a) BEP (algebraic)
Total cost $C(x)=15{,}000+2x$ . Revenue $R (x) = 12 x$ .
Set equal: $\Rightarrow 10x=15{,}000 \Rightarrow x=1{,}500.$
So BEP = 1,500 staplers.

(b) BEP (graphical)
Plot $R (x) = 12 x$ and $C(x)=15{,}000+2x$ ; intersection at $x=1{,}500$ . (Same intersection as algebraic.)

(c) Total cost at BEP
$C(1500)=15{,}000+2(1500)=15{,}000+3{,}000=18{,}000.$

(d) Total sales revenue at BEP
$R(1500)=12(1500)=18{,}000.$

(e) Profit at BEP
Profit = Revenue − Cost = $18,000 − $18,000 = $0 (by definition at BEP).

3.Solution manual publisher

Given: variable cost per manual = $4, fixed cost = $15,000, price = $29.99 per manual.

(a) Sales revenue equation
$R (x) = 29.99 x$

(b) Total cost equation
$C(x)=15{,}000+4x$

(c) Profit if 2,000 manuals are published
Profit $P(x)=R(x)-C(x)=29.99x-(15{,}000+4x)=(29.99-4)x-15{,}000=25.99x-15{,}000.$
For $x=2{,}000$ : $P(2000)=25.99(2000)-15{,}000=51{,}980-15{,}000=36{,}980.$
So profit = $36,980.

(d) BEP (algebraic)
Set $\Rightarrow 25.99x=15{,}000 \Rightarrow x=\dfrac{15{,}000}{25.99}$ .
Compute: $x≈577.145x\approx 577.145$ . Because you can’t sell a fractional manual, the publisher must sell 578 manuals to exceed break-even (577 manuals gives a tiny shortfall). Exact break-even point is ≈ 577.15 manuals.

(e) Method preference
Again, algebraic for the exact break-even number; graphical is useful to visualize margin and to present to others.

4.AirAsia regional route

Given: fixed cost per season = $12,000,000, variable cost per passenger = $24, average fare = $59.

Let $p$ = number of passengers.

(a) Sales revenue equation
$R (p) = 59 p$

(b) Total cost equation
$C(p)=12{,}000{,}000 + 24p$

(c) Profit if 420,000 passengers are carried
Profit $P(p)=R(p)-C(p)=(59-24)p – 12{,}000{,}000 = 35p – 12{,}000{,}000.$
For $p=420{,}000$ : $P=35(420{,}000)-12{,}000{,}000 = 14{,}700{,}000 – 12{,}000{,}000 = 2{,}700{,}000.$
So profit = $2,700,000 for the season.

(d) BEP (algebraic)
Set $\Rightarrow 35p = 12{,}000{,}000 \Rightarrow p = \dfrac{12{,}000{,}000}{35} \approx 342{,}857.1429.$
So break-even ≈ 342,858 passengers (round up to whole passengers).

(e) BEP graphically
Plot $R (p) = 59 p$ and $C(p)=12{,}000{,}000+24p$ . They intersect at ~342,857 passengers.
Preference: algebraic for an exact number and quick planning; graphical for presentations and intuition (showing how far above BEP a proposed load is).

Quick summary table (key BEP results)

Exercise 1 (books): BEP = 5,000 copies.
Exercise 2 (staplers): BEP = 1,500 units.
Exercise 3 (manuals): BEP ≈ 577.15 → 578 manuals to be safe.
Exercise 4 (AirAsia): BEP ≈ 342,857.14 → 342,858 passengers to break even.