b) Suppose the total cost function for rolls and pies is,

TC = 10x₁+ x₁x₂+10x₂

where and denote the quantities of rolls and pies, respectively. If and denote the corresponding prices, then the demand equations are:

P₁ = 50 - x₁ + x₂ and P₂ = 30 + 2x₁ - x₂

If James sticks to his idea of making and selling 100 rolls and pies in total per day, how many of rolls and pies each should he make in order to maximize the profit of a particular day?