Answer:
The correct option is (B) 250.
Step-by-step explanation:
A plant can manufacture 100 golf clubs per day for a total daily cost of $7,800.
And 120 golf clubs per day for a total daily cost of $8,400.
Let <em>X</em> = number of golf clubs manufactured per day.
Let <em>Y</em> = total cost of manufacturing golf clubs per day
It is provided that:
(<em>x</em>₁, <em>y</em>₁) = (100, 7800)
(<em>x</em>₂, <em>y</em>₂) = (120, 8400)
Form the least square regression line using two-point form as follows:
![(y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})](https://tex.z-dn.net/?f=%28y-y_%7B1%7D%29%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%5C%20%28x-x_%7B1%7D%29)
![(y-7800)=\frac{8400-7800}{120-100}\ (x-100)\\\\(y-7800)=30\times (x-100)\\\\y-7800=30x-3000\\\\y=30x+4800](https://tex.z-dn.net/?f=%28y-7800%29%3D%5Cfrac%7B8400-7800%7D%7B120-100%7D%5C%20%28x-100%29%5C%5C%5C%5C%28y-7800%29%3D30%5Ctimes%20%28x-100%29%5C%5C%5C%5Cy-7800%3D30x-3000%5C%5C%5C%5Cy%3D30x%2B4800)
The least square regression line to estimate the total daily cost of <em>x</em> golf clubs manufactured daily is:
<em>y</em> = 30 <em>x</em> + 4800
Compute the number of golf clubs manufactured if the total daily cost is $12,300 as follows:
![y = 30 x + 4800\\12300=30x+4800\\30x=7500\\x=250](https://tex.z-dn.net/?f=y%20%3D%2030%20x%20%2B%204800%5C%5C12300%3D30x%2B4800%5C%5C30x%3D7500%5C%5Cx%3D250)
Thus, the correct option is (B).