Question

1, The cost of making 14 tables is $2,000. The cost of making 22 tables is $2,640. What is the cost per table?

Write a linear equation that tells you the total cost, C , of making x tables: C =

What is the total cost of making 17 tables? $

2, The cost of making 14 chairs is $1,090. The cost of making 26 chairs is $1,570.

What is the cost per chair?

Write a linear equation that tells you the total cost, C , of making x chairs: C =

If your total cost is $2,610, how many chairs did you make?

3,

Answer 1

First of all find variable cost and fixed cost

Variable cost per unit=change in cost /change in quantity=($2000-2640)/(14-22)=$80 per table

Now $80×14 tables=$1,120=variable cost

Fixed cost=$2000-1120=$880

Again $80×22 tables=$1760=variable cost

Fixed cost=$2640-1760=$880

Fixed cost should remain same.

Now linear equation

Total cost includes both variable and fixed cost.

So,

C= X × Variable cost + Fixed cost

Where C= Total cost

X= Units of output i.e. number of tables

Therefore in this case c=X ×80 +880

Now total cost of making 17 tables

Using above equation

C=17×80+880= $2,240

Now calculation for chairs.

Here also similar method as done for table is followed.

First of all find fixed cost and variable cost

Variable cost per unit=change in cost/change in quantity

($1090-1570)/(14-26)=$40 per chair

Now, $40×14 chairs=$560 variable cost

Fixed cost=1090-560=$530

Again,

$40×26chairs=$1040=variable cost

Fixed cost=$1570-1040=$530

Fixed cost should remain same

Now linear equation

C=X × variable cost+Fixed cost

Where c=total cost

X=number of chairs

Therefore , C=X × 40 +530 in this case

Using above equation

2610= X ×40+ 530

X=(2610-530)/40

X=52 chairs