A plant can manufacture 50 golf clubs per day at a total daily cost of $4669 and 60 golf clubs per day for a total cost of $5269. (A) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs.

C=60x+600

Explanation:

A linearly related equation is one that can be expressed in the form;

y=mx+b,

where;

y=C=Cost variable that linearly related to x

x=number of golf clubs produced linearly related to y

b=y-intercept, the value of y when x=0

m=slope

The value of m can be calculated using the formula;

m = (y2-y1) / (x2-x1)

where;

y2=C2=5269, x2=60

y1=C1=4669, x1=50

replacing;

m = (5269-4669) / (60-50) = 600/10=60

We can derive the following equations;

C2=mx2+b ... equation 1

C1=mx1+b ... equation 2

replacing values of C2, x2 and m in equation 1;

5269 = (60*60) + b

b=5269-3600=600

since m and b are constant values that don't vary we can include them in the equations 1 and 2;

C=mx+b

where;

m=60

b=600

replacing;

C=60x+600