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)

What is the product of 27 and 13?

What is the limit as x approaches infinity of (sqrt(x^2 + 2x) - x)?

What is the equation of an ellipse with major axis 8 and minor axis 6?

New questions in Mathematics

Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.

³√12 x ⁶√96

4X^2 25

224 × (6÷8)

A job takes 9 workers 92 hours to finish. How many hours would it take 5 workers to complete the same job?

4x-3y=24 and 5x-2y=9 solve by elimination

4. Show that if n is any integer, then n^2 3n 5 is an odd integer

A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?

prove that if n odd integer then n^2+5 is even

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

In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left. How many peppers and carrots were there initially?

Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.

(2m+3)(4m+3)=0

If a|-7 and a|9, then a|-63

A bag has 4 green lollipops, 3 white lollipops, and 1 black lollipop. What is the probability of drawing a white lollipop?

Subjects are randomly assigned to one of three specialties for a 3-month rotation, and at the end of that rotation, they are given a test that measures moral development. The scores are listed below, where a high score represents high moral development and a low score represents low moral development. Orthopedics Pediatrics Oncology 77 63 54 84 93 97 66 97 76 44 76 65 59 45 91 40 88 68 28 74 54 M = 56.86 M = 76.57 M = 72.14 What is Nt?

Calculate the difference between 407 and 27

Total Users with an active Wise account = Total Active Users + Total Users who haven’t transacted Total Active Users = Total MCA Users + Total Send Users = Total New Users + Retained Users Total New Users = New Send Users + New MCA Users Total MCA Users = New MCA Users + Retained Users who transacted this month via MCA Total Send Users = New Send Users + Retained Users who transacted this month via Send Send CR = Total Send Users / Total Users with an active Wise account MCA CR = Total MCA Users / Total Users with an active Wise account New Send CR = New Send Users / New Profiles Created in Month New MCA CR = New MCA Users / New Profiles Created in Month We have recently witnessed a drop in MCA conversion, but send user conversion is stable, can you help explain why?

Calculate the pH of a solution obtained by mixing 100ml of 0.2M HCl with 100ml of 0.1M NaOH

Let A denote the set of all people who were alive in 2010. Let B denote the set of all real numbers. Let f assign, to each person in A, their weight during the year 2010. Is f a function? Explain in complete sentences.

You might be interested in