A factory has a linear cost function

. where b represents fixed costs and a represents the labor and material costs of making one item, both in thousands of dollars. If property taxes (part of the fixed costs) are increased by $28,000 per year, what effect does this have on the graph of the cost function?

A factory has a linear cost function, where b represents fixed costs and a represents the labor and material costs of making one item. So

y = ax + b, where y is total cost n x is no. of items

property tax is part of b so its increase will add 28 to b, the new cost function becomes:

y' = ax + b' where b' = b + 28

the line graph moves up by 28 in the y-direction

Cost function, f (x) = ax + b

If b goes up by 28 (thousands of dollars), the graph of cost function will move up by 28 in y.