A husband and wife each have 10 hours per week to devote to leisure activities, and together they have $100 of disposable income to spend. Going to a movie takes 3 hours for each person and costs $40. The wife likes to watch TV at home, which is free but takes 1 hour of her time per TV show. The husband likes paint, which costs $10 and takes 3 hours of his time per painting. Let p represent the number of paintings the husband does, t the number of shows the wife watches, and m the number of movies they see together. (These do NOT need to be integers). (a) Using matrix notation, write down the restrictions on how they spend their leisure time, assuming that they use all of their leisure time and all of their disposable income. 3 marks (b) Solve for p, m, and t by nding the inverse of the matrix and using the adjoint method. 11 marks