Perfect substitutes almost always have boundary solutions, which are found in a different way than interior optima. The demand functions from perfect substitutes are contingent; specifically, they depend on the slopes of the indifference curves and the budget line.
Consider a utility function (x₁,x₂) = ax₁ + bx₂ and a general-form budget line p₁x₁ + p₂x₂.
If the absolute value of the slope of the indifference curve, a/b, is greater than the absolute value of the slope of the budget line, P₁/P₂ the consumer will find it optimal to consume
Choose one:
A all of good 1 she can afford and none of good 2.
B. all of good 2 she can afford and none of good 1.
C. a combination of goods 1 and 2 such that exactly half her income is spent on each good.
D. any combination of goods 1 and 2 she can afford.