The market for round trip airline travel from Madison to Cleveland over the Memorial Day holiday consists of two types of customers. Let X₁denote the demand for airline tickets by students, and let X₂denote the demand for airline tickets by non-student adults. Let the price of a round trip ticket be denoted by P_x, and suppose that everyone who purchases a ticket pays the same price. The demand functions of the two customer groups has been determined as follows

X₁= 1900 -30P_x

X₂= 4500 -90P_x

(a) What is the total market demand for airline tickets, as a function ofby P_x? Keep in mind that the total demand is the sum of the group demands (students plus non student adultsthis is in a lecture). I suggest you calculate the demand forX₁andX₂ and the total for X₁+X₂. This question requires you to show your work and produce a mathematical answer.

(b) Suppose that the price-elasticity of demand by students, at the priceby

P_x, is-2. What is the price-elasticity of demand bynon-student adults? (consider raising the price by $1 to address this question). This question requires you to show your work and produce a mathematical answer.

(c) At what price is the total revenue (for the entire market) maximized? This question requires you to show your work and produce a mathematical answer.