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

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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

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Andrea

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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

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