Please write a solutions with formulas and explanations.

A student wishes to earn some pocket money during his semester break. He thinks hard and comes up with the idea of buying early tickets for theater shows and selling them to last-minute customers who cannot find tickets. He can buy early tickets for around 40TL each. Late customers are usually ready to pay 75 TL per ticket. Normally, unsold tickets are of no value, however, the student has good contacts with the ticket office attendant. So, if the student has left over tickets when the show starts, the attendant at the ticket office pays him 20 TL per ticket. Assume, now that the student wants to be more precise in estimating the demand and keeps a record of demand on each day. After careful analysis, he identifies that his demand obeys the triangular distribution with lower limit a, upper limit b and mode c, where a