The problem asks to find the linear equation $Y = a + bX$ based on the given data table, where $X$ represents time and $Y$ represents supply. We need to calculate the values of $a$ and $b$ using the given formulas.

1. Problem Description

The problem asks to find the linear equation $Y = a + bX$ based on the given data table, where $X$ represents time and $Y$ represents supply. We need to calculate the values of $a$ and $b$ using the given formulas.

2. Solution Steps

Step 1: Calculate $b$ using the formula:

$b = \frac{\Sigma xy - n \bar{x} \bar{y}}{\Sigma x^2 - n(\bar{x})^2}$

Given:

$\Sigma xy = 3,252,873$

$n = 5$

$\bar{x} = 3$

$\bar{y} = 215,136$

$\Sigma x^2 = 55$

Plugging in the values:

$b = \frac{3,252,873 - 5(3)(215,136)}{55 - 5(3)^2}$

$b = \frac{3,252,873 - 3,227,040}{55 - 45}$

$b = \frac{25,833}{10}$

$b = 2,583.3$

Step 2: Calculate $a$ using the formula:

$a = \bar{y} - b\bar{x}$

Given:

$\bar{y} = 215,136$

$b = 2,583.3$

$\bar{x} = 3$

Plugging in the values:

$a = 215,136 - 2,583.3(3)$

$a = 215,136 - 7,749.9$

$a = 207,386.1$

Rounding $a$ to the nearest whole number, $a = 207,386$.

Step 3: Write the linear equation.

$Y = a + bX$

$Y = 207,386 + 2,583.3X$

3. Final Answer

$Y = 207,386 + 2,583.3X$