Question

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. Assuming that the daily cost and production are linearly related, find the number of golf clubs manufactured if the total daily cost is $12,300. * A. 167 B. 250 C. 410 D. 4,800

Answer 1

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:

$(y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})$

$(y-7800)=\frac{8400-7800}{120-100}\ (x-100)\\\\(y-7800)=30\times (x-100)\\\\y-7800=30x-3000\\\\y=30x+4800$

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:

$y = 30 x + 4800\\12300=30x+4800\\30x=7500\\x=250$

Thus, the correct option is (B).