Respuesta :
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 X = number of golf clubs manufactured per day.
Let Y = total cost of manufacturing golf clubs per day
It is provided that:
(x₁, y₁) = (100, 7800)
(x₂, y₂) = (120, 8400)
Form the least square regression line using two-point form as follows:
[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})[/tex]
[tex](y-7800)=\frac{8400-7800}{120-100}\ (x-100)\\\\(y-7800)=30\times (x-100)\\\\y-7800=30x-3000\\\\y=30x+4800[/tex]
The least square regression line to estimate the total daily cost of x golf clubs manufactured daily is:
y = 30 x + 4800
Compute the number of golf clubs manufactured if the total daily cost is $12,300 as follows:
[tex]y = 30 x + 4800\\12300=30x+4800\\30x=7500\\x=250[/tex]
Thus, the correct option is (B).
