Download 1) We are thinking of opening a Broadway play, I Love You, You`re

1) We are thinking of opening a Broadway play, I Love You, You’re Mediocre, Now Get Better! It will cost $5
million to develop the show. There are eight shows per week, and we project the show will run for 100 weeks.
It costs $1000 to open the theatre each night. Tickets sell for $50.00, and we earn an average of $1.50 profit per
ticket holder from concessions. The theatre holds 800, and we expect 80% of the seats to be full. Use data tables
to display and analyze your results for parts b and c.
a. Given our other assumptions, how many weeks will the play have to run for us to earn a 100% return on the
play’s development cost?
b. Given our other assumptions, how does an increase in the percentage of seats full affect profit?
c. Given our other assumptions, determine how a joint change in the average ticket price and number of weeks
the play runs influence profit (use a two-way data table to present the results).
2) Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3 units of wood.
A desk contributes $40 to profit, and a chair contributes $25. Marketing restrictions require that the number of
chairs produced be at least twice the number of desks produced. There are 20 units of wood available.
a. Provide an algebraic formulation where you clearly define your decision variables and state your formulation.
(Hint: let X1 be the number of desks to produce and X2 be the numbers of chairs to produce).
b. Use Solver to maximize Furnco’s profit.
c. Confirm graphically that the solution in part b maximizes Furnco’s profit.
3) To answer this problem, refer to the link above.
a. Thinking about what we discussed in the first lecture, reference the characteristics of different problems
solved by operations research techniques. The problem referred to in the article would require which technique
to solve it, e.g., statistics, optimization, or simulation. Why?
b. The title of the article is “The Problem of the Traveling Politician.” What class of mathematical problems is
this one closely related too?
c. The article does not provide the objective of this problem. What do you think the objective of the problem is
(be specific, but a mathematical formulation is not necessary)?
d. What are the problem constraints (be specific, but a mathematical formulation is not necessary).
e. What is the solution given in