Question

The manager of a furniture factory finds that it costs $3000 to manufacture 50 chairs in one day and $4800 to produce 250 chairs in one day. (a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.

Answer 1

Total cost= 2,550 + 9*x

Step-by-step explanation:

Giving the following information:

The manager of a furniture factory finds that it costs $3000 to manufacture 50 chairs in one day and $4800 to produce 250 chairs in one day.

We need to calculate the fixed and variable costs to determine the function. We will use the high-low method:

Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)

Variable cost per unit= (4,800 - 3,000) / (250 - 50)= $9 per chair

Fixed costs= Highest activity cost - (Variable cost per unit * HAU)

Fixed costs= 4,800 - (9*250)= 2,550

Fixed costs= LAC - (Variable cost per unit* LAU)

Fixed costs= 3,000 - (9*50)= 2,550

Now, we can formulate the function

Total cost= fixed cost + variable cost

Total cost= 2,550 + 9*x

x= number of chairs