The Power of Calculus in Financial Modeling and Risk Management Mathematics is an essential tool in finance, and calculus is one branch of mathematics that has a particular significance in the field. Calculus is used to model and analyze financial data, as well as to assess and manage risk. In this essay, we will explore the ways in which calculus is used in financial modeling and risk management, and how it helps to inform investment decisions and guide financial strategy.

1. Equation and Its Application in Daily Business Calculation
Course Name: Mathematics for Decision
Course Code: BUS 7102
Submitted by:
Tasnim Jahan Promi
ID: 23230333050
Batch: 33rd
Section: A
Bangladesh University of Professionals
Submitted to:
Prof. Dr. MD Showkat Ali
Faculty of Business Studies (FBS)
Bangladesh University of
Professionals

2. Equation and Its Application in Daily Business Calculation
Total cost: Total cost is the sum of fixed cost and variable cost.
Variable cost: Variable cost refers to the component of cost that changes as the
number of units produced changes.
Fixed cost: Fixed cost refers to the component of cost that does not vary with
the number of units produced.
Marginal cost: Marginal cost is the variable cost per unit or the slope of the total
cost function.
Average cost: Average cost is the total cost per unit produced.
If we interpret the equation y = 3x + 5, letting y be the total cost of producing x
units, the fixed cost is $5, variable cost is $3x, marginal cost or the variable cost
per unit is $3 and the average cost is y/x.

3. Equation and Its Application in Daily Business Calculation
Supply function: Supply function expresses the supplied quantity as a function of
price per unit.
Demand function: Demand function expresses the quantity demanded as a
function of price per unit.
Cost function: Cost function expresses cost as a function of quantity produced.
For example, C(x) = mx + b, where C(x) is the cost of producing x units, mx is the
variable cost and b is the fixed cost.
Revenue function: Revenue function R(x) = p(x) expresses the amount of money,
R(x) received for selling x units at $p per unit.
Profit function: Profit function is the difference between the revenue function and
the cost function. P(x) = R(x) – C(x). If the difference is negative, it will be loss
function.
Break-even: Break-even is a circumstance where revenue equals to the cost and
so there is no profit and no loss. At break-even, R(x) = C(x).

4. Equations
• FC = Fixed cost is the cost of number of unit
production
• VC = Variable cost is the cost of during production
• TC = FC+ VC
• Cost function C(x) = VC + FC
• Revenue function R(x) = Selling price/unit X num of
unit sold
• Profit function P(x) = R(x) – C(x)
• Loss function P(x) = C(x) – R(x)
• Break even point = R(x) = C(x)
• MC = VC / no. of unit
• AC = TC / no. of unit
• Linear equation: Y= ax+b
Distance of two point: (X-X1/X1-X2), (y-y1/y1-y2)

5. A factory produces 200 bulbs for a total cost of $800 and 400 bulbs for a total cost of $1200. Given that the cost
curve is a straight line, find the equation of the straight line and use it to find the cost of producing 300 bulbs.
Let the cost be y and the number of the bulbs be x.
The linear equation for the total cost in terms of the number of bulbs would be
𝑦−1200 / 1200−800 = 𝑥−400 / 400−200
⇒ 𝑦−1200 / 400 = 𝑥−400 200
⇒ 𝑦−1200 / 2 = 𝑥 − 400
⇒ 2x – 800 = y – 1200
⇒ 2x – y + 400 = 0 (Answer)
If x = 300,
2(300) – y +400 = 0
⇒ y = 1000
So, The cost of producing 300 bulbs is $1000. (Answer)

6. An agency rents bus for one day and charges $44 plus 20 cents per mile the bus is driven.
(a) Write the equation for the cost of one day’s rental, y, in terms of x, the number of miles driven.
(b) Interpret the slope and the y- intercept.
(c) What is the renter’s average cost per mile if a bus is driven 100 miles? 200 miles?
Solution –
(a)
The desired equation is
y = 0.20x + 44 (Answer)
(b)
The slope of the equation is 0.20. It means for additional one mile the bus is driven, there would be an
additional charge of $0.20.
The y-intercept is 44. It means if a bus is rented but not used, there will still be a fixed charge of $44.

7. (c)
If x = 100,
y = 0.20(100) + 44=64
∴ The average cost for 100 miles = 64 ÷100 = 0.64 ( answer)
If x = 200,
Y = 0.20 (200) + 44 = 84
∴ The average cost for 200 miles = 84 ÷200 = 0.42( answer)
Thank You