Question

The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4400 to produce 300 chairs in one day.
(a) Assuming that the relationship between cost C and the number of chairs produced x is linear, find an equation that expresses this relationship.

Answer 1

The equation will be of the form C = mx + b where C is the cost per chair, x is the number of chairs produced per day, m is the slope of the line and b is a constant.
When x = 100, C = 2200/100 = $22 per chair
When x = 300, C = 4400/300 = $14.67 per chair
M can be found from the following formula:
\[m=\frac{y _{1}-y _{2}}{x _{1}-x _{2}}=\frac{C _{1}-C _{2}}{x _{1}-x _{2}}=\frac{22-14.67}{100-300}=you\ can\ calculate\]
When you have found m, substitute the value and values of C and x into C = mx + b and solve to find the value of b.

Answer 2

i think it might be
(C-2200) = ((4400-2200)/(300-100) ) * (x-100)
C-2200=((2200/200)) *(x-100)
C=11x-1100+2200
C=11x +1100

Answer 3

@kropot72 You were a bit too clever for your own good. The problem is asking for the relationship between total cost and chairs produced, not cost per chair. Your line will have a negative slope because the cost per chair goes down as volume goes up, but the total cost has a positive slope as we never have a negative marginal cost to produce another chair.

Answer 4

Though reading the problem again, reasonable people could differ on the meaning of "cost C", I'll admit!

Answer 5

@whpalmer4 I think your interpretation is what was wanted by the setter of the question.

Answer 6

I'd give medals to both of you if I could :-)