Find Variable Cost per Unit I am trying to do this problem, and I am  not getting the answer.
I need to find the fixed cost of system 1, and system 2.
I know that the fixed cost will be the y-intercept of the equation.
Fixed cost for system 1 is 1000, and fixed cost for system 2 is $5000.
When I tried to find the variable cost per map dispensed, I am not getting the answer.
I know that the variable cost changes with the output. Therefore, it is the slope of the equation. In this case, the variable cost for system 1 is supposed to be 0.90, and the variable cost per map dispensed for system 2 is 0.1. However, the solutions manual shows that the variable cost per map dispensed for system 1 is 0.8, and variable cost per map dispensed for system 2 is 0.16.
Did I do something wrong?
Based on the information you have given, both the solution manual and your solution are wrong. You are correct that the fixed cost for system I is 1. Variable cost is given by $$VC(x)=TC(x)-FC.$$ The variable cost for system I is therefore equal to $0.9x$. Note that the variable cost depends on $x$! For system II the variable cost is $0.1x$.

You appear to have confused variable cost with marginal cost. Variable cost is the part of the total cost that changes with quantity; marginal cost is, roughly, the cost of producing one more unit (and is given by the slope of the total cost curve). Thus, the marginal cost of system I is $0.9$ and the marginal cost of system II is $0.1$.