A movie theater sells three kinds of tickets- children (for $10), adult (for $16

Question

A movie theater sells three kinds of tickets- children (for $10), adult (for $16), and seniors (for $12). The number of children tickets has E[Cl-45 and MC-100. The number of adult tickets has E[A]-137 and VA-610. Finally, the number of senior tickets has E[S]:34 and V[S]-90. You may assume the number of tickets in each group is independent. Any particular movie costs $1100 to show, regardless of the audience size. a. b. Write a formula relating C, A, and S to the theater's profit P for a particular movie. Compute E[P] and ViP].

Explanation / Answer

(a)

Profit = Selling Price - Cost Price

Cost Price = 1100

Selling Price = Price of Adult tickets * Count   +   Price of Children's tickets * Count + Price of Senior's tickets * Count

Profit (P) = ((E(A) * 16 )+(E(C)*10)+(E(S)*12)) -1100

......................................................................

(b)

E(P) = E(Selling price) - Cost price

E(P) = (137*16   +    45*10    +   34*12 )- 1100

       = 3050 -1100 = 1950

V(P) = (Standard Deviation in Profit)^2

V(A) = 610 ; Standard Deviation = 24.69

V(C) = 100 ; Standard Deviation = 10

V(S) = 90 ; Standard Deviation = 9.48

Standard Deviation in Selling Price = (24.69*16) +(10*10) + (9.48*12)

                                        = 608.8

Variance in Selling Price = 370637.44

Profit = SP - CP

CP = constant

So, Variance in SP = Variance in Profit = 370637.44

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.