Question

Application 1 – 30 points The company “PEP Ltda.” presents information about its inventory and sales costs, both in thousands of pesos and on a semi-annual basis from 2015 to 2018. This information is presented in the following table: Semester Costs (X) Sales (Y) S1 – 2020 $12,000 $40,200 S2 – 2020 $15,000 $45,000 S1 – 2021 $11,250 $38,000 S2 – 2021 $13,350 $39,500 S1 – 2022 $17,400 $46,000 S2 – 2022 $13,800 $38,000 S1 – 2023 $15,750 $44,300 S2 – 2023 $14,400 $37,800 a) Determine the equation that estimates sales for the following periods using the MCO method. Determine and interpret the coefficients and the general and individual analysis of the regression (10 points). b) Suppose that the company generates a net profit equal to 20% of sales. If information is available on inventory costs for the next 3 years, determine the net profit obtained by the company for each period (20 points). Semester Costs (X) S1 – 2024 $16,500 S2 – 2024 $17,400 S1 – 2025 $18,000 S2 – 2025 $18,750 S1 – 2026 $19,650 S2 – 2026 $20,550

likes

267 views

Answer to a math question Application 1 – 30 points The company “PEP Ltda.” presents information about its inventory and sales costs, both in thousands of pesos and on a semi-annual basis from 2015 to 2018. This information is presented in the following table: Semester Costs (X) Sales (Y) S1 – 2020 $12,000 $40,200 S2 – 2020 $15,000 $45,000 S1 – 2021 $11,250 $38,000 S2 – 2021 $13,350 $39,500 S1 – 2022 $17,400 $46,000 S2 – 2022 $13,800 $38,000 S1 – 2023 $15,750 $44,300 S2 – 2023 $14,400 $37,800 a) Determine the equation that estimates sales for the following periods using the MCO method. Determine and interpret the coefficients and the general and individual analysis of the regression (10 points). b) Suppose that the company generates a net profit equal to 20% of sales. If information is available on inventory costs for the next 3 years, determine the net profit obtained by the company for each period (20 points). Semester Costs (X) S1 – 2024 $16,500 S2 – 2024 $17,400 S1 – 2025 $18,000 S2 – 2025 $18,750 S1 – 2026 $19,650 S2 – 2026 $20,550

$Expert avatar$

Andrea

4.5

86 Answers

a)
1. Calcular la media de los costos y ventas (en miles de pesos):

\bar{X} = \frac{12{,}000 + 15{,}000 + 11{,}250 + 13{,}350 + 17{,}400 + 13{,}800 + 15{,}750 + 14{,}400}{8} = 14{,}368.75

\bar{Y} = \frac{40{,}200 + 45{,}000 + 38{,}000 + 39{,}500 + 46{,}000 + 38{,}000 + 44{,}300 + 37{,}800}{8} = 41{,}225

2. Calcular la pendiente (b) y la intersección (a) de la ecuación de regresión:

b = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sum (X_i - \bar{X})^2} = 1.29375

a = \bar{Y} - b\bar{X} = 22165.02

Ecuación de regresión:

Y = 22165.02 + 1.29375X

b)
1. Para los costos futuros, se usa la ecuación de regresión para estimar las ventas:

Y_{2024_1} = 22165.02 + (1.29375 \times 16{,}500) = 39{,}397.425

Y_{2024_2} = 22165.02 + (1.29375 \times 17{,}400) = 40{,}051.2

Y_{2025_1} = 22165.02 + (1.29375 \times 18{,}000) = 40{,}462.515

Y_{2025_2} = 22165.02 + (1.29375 \times 18{,}750) = 41{,}116.825

Y_{2026_1} = 22165.02 + (1.29375 \times 19{,}650) = 41{,}565.015

Y_{2026_2} = 22165.02 + (1.29375 \times 20{,}550) = 42{,}013.2

2. Calcular la utilidad neta (20% de las ventas):

U_{2024_1} = 0.2 \times 39{,}397.425 = 7879.485

U_{2024_2} = 0.2 \times 40{,}051.2 = 8010.24

U_{2025_1} = 0.2 \times 40{,}462.515 = 8092.503

U_{2025_2} = 0.2 \times 41{,}116.825 = 8190.665

U_{2026_1} = 0.2 \times 41{,}565.015 = 8313.003

U_{2026_2} = 0.2 \times 42{,}013.2 = 8435.34

Frequently asked questions (FAQs)

Math Question: Graph the following inequality on a coordinate plane: y > 2x - 3. Which region satisfies this inequality?

Question: Solve the equation: 3x^2 + 10x - 8 by factoring and using the distributive property.

Math question: What is the limit of (x^2 - 4) / (x - 2) as x approaches 2?

New questions in Mathematics

calculate the derivative by the limit definition: f(x) = 6x^3 + 2

How many percent is one second out a 24 hour?

Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)

Write 32/25 as a percent

58+861-87

If f(x) = 3x 2, what is the value of x so that f(x) = 11?

-3x 2y = -6; -5x 10y = 30

(-5/6)-(-5/4)

Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?

If 0101, what is the binary representation of the 4x16 decoder output?

3.24 ÷ 82

Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9 Enter the value of the function, not the value of x

If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13

a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?

Today a father deposits $12,500 in a bank that pays 8% annual interest. Additionally, make annual contributions due of $2,000 annually for 3 years. The fund is for your son to receive an annuity and pay for his studies for 5 years. If the child starts college after 4 years, how much is the value of the annuity? solve how well it is for an exam

Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].

A grain silo has a height of 8.8m with a 11.4m diameter. If it is filled 0.5% of it's volume, how much grain (m^3) is stored in the silo? (0 decimal places)

Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?

Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2

Find the rule that connects the first number to the second number of each pair. Apply the rule to find the missing number in the third pair. (18 is to 22) (54 is to 26) (9 is to ?)

You might be interested in