Find what is the maximum amount that they could pay for sofa

Question

Problem

Albert and Beth are thinking of buying a sofa. Albert's utility function is u_a(s; m_a) = [1 + s]m_a and Beth's utility function is u_b(s; m_b)=[2 + s]m_b, where s = 0 if they don't get the sofa and s = 1 if they do, and m_a and m_b are the amounts of money they have respectively to spend on private consumption. Albert and Beth each have a total of w = 100 (in $) to spend. What is the maximum amount that they could pay for the sofa and still both be better than without it?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.