📘 business mathematics

1. **Problem Statement:** A company has two investment portfolios, X and Y. Portfolio X has a return of $\frac{3}{5}$ on investment, and Portfolio Y has a return of $\frac{2}{5}$ o

1. **Problem Statement:** In a survey of 600 students, percentages of students liking football, hockey, and basketball are given along with overlaps. We need to find:

1. **Problem Statement:** a) Find the market equilibrium price and quantity given demand equation $p - 3q = 22$ and supply equation $q^2 + 2p + 4q = 100$. Then find total revenue,

1. **Problem Statement:** Find the market equilibrium price and quantity given demand and supply equations, then find total revenue.

1. **Problem Statement:** a) Find the market equilibrium price and quantity given demand equation $p = 3q - 22$ and supply equation $q^2 + 2p + 4q = 100$.

1. **Problem Statement:** Find the market equilibrium price and quantity given the demand equation $p - 3q = 22$ and the supply equation $q^2 + 2p + 4q = 100$, where $p$ is price a

1. **Problem:** Three people invested Rs. 900, Rs. 600, and Rs. 300 in a business. How should they share a profit of Rs. 900? 2. **Formula:** Profit is shared in the ratio of inves

1. **Problem 1: Total Revenue and Profit in Each Market Using Matrix Algebra** Given sales volumes for products P, Q, R in markets A and B:

1. **Find the maximum and minimum values of the function** $$f(x) = 3x^2 - 2x^3 - 12x + 8$$ Step 1: State the problem: We want to find the maximum and minimum values of the cubic f

1. **Find the maximum and minimum value of the function** Given function: $$f(x) = 3x^2 - 2x^3 - 12x + 8$$

1. **Problem (a):** Find the number of distinct permutations of the letters of the word MATHEMATICS. - The word MATHEMATICS has 11 letters.

1. **Find the 20th term of an A.P. with first term 5 and common difference 4.** The nth term of an arithmetic progression (A.P.) is given by:

1. Problem statement: We are given market equilibrium for pencil prices and quantities. At price Rp 1,000, demand equals supply at 800 pencils. When price rises to Rp 1,500, demand

1. Problem 1 – Return on Investment (ROI): The company invested 1,000,000 and generates annual operating income of 250,000.

1. **State the problem:** The Miers Company produces engines to be shipped to two plants, Plant I and Plant II. Plant I requires at least 45 engines, Plant II requires at least 32

1. Problem 1: Maximize production given budget constraints. 1.1 The production function is $$N(x,y) = 10 x^{0.6} y^{0.4}$$ where $x$ is labor units and $y$ is capital units.

1. **Find the maximum and minimum value of the function** $$f(x) = 3x^2 - 2x^3 - 12x + 8$$

1. Find the maximum and minimum value of the function $f(x)=2x^3 - 3x^2 - 12x + 8$. 2. A mixed hockey team containing 5 men and 6 women is to be chosen from 7 men and 9 women. Calc