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

85 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 measure of the third angle in a triangle if the first angle measures 35° and the second angle measures 75°?

What is the variance of the following data set: 12, 15, 18, 21, 24?

Math question: Solve the cubic equation x^3 + 4x^2 - 7x - 10 = 0.

New questions in Mathematics

A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.

Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:

The ratio of tomatoes to red apples is 2:5. If there are 20 tomaoes in the garden, how many red apples are there?

Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]

Divide 22 by 5 solve it by array and an area model

-4y-6(2z-4y)-6

Pedro had 80% of the amount needed to buy a game. Of this amount, you spent 15% on a watch and therefore, you will need to add another R$640.00 to purchase this game. Is the value of the game?

Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current standard treatment shall be compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life questionnaire at 8 weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded a clinically important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you assume that the change in of the summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both treatments. How many patientes would one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?

Let A, B, C and D be sets such that | A| = |C| and |B| = |D|. Prove that |A × B| = |C × D|

Quadratic equation 2X = 15/X + 7

The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?

A company made 150,000 in the first year 145,000 in the second 140,000 in the third year successively during the first decade of this company's existence it made a total of

A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.

Solve for B write your answer as a fraction or as a whole number. B-1/7=4

simplify w+[6+(-5)]

For how long does the principal amount of €7,537 bring the same interest as the principal amount of €12,345 invested for 8 months? Interest calculation is simple and decursive.

Arturo had hospitalization expenses of $8,300. Your policy for medical expenses Seniors have a deductible of $500 and expenses are paid at a 20% coinsurance. These are the first expenses ever this year, how much will Arturo have to pay in your bill for hospitalization expenses?

7-1=6 6x2=12 Explain that

2p-6=8+5(p+9)

To apply a diagnostic test, in how many ways can 14 students be chosen out of 25? if the order does not matter

You might be interested in