Problemas de investigacion de operaciones

OPERATIONS RESEARCH I IN00841

Partial Exam No.1 (Draft Version)
January 27, 2011

1. Use the graphical approach to solve the problem:

Maximize[pic],
subject to
[pic]
and
[pic].
ANSWER: [pic]2. The firm Whitt Window has only three employees who make two types of windows by hand: with a wooden frame and with an aluminum frame. The profit is $60 per each window with a wooden frameand $30 per every one with an aluminum frame. Doug makes wooden frames and can finish 6 a day. Linda makes 4 aluminum frames per day. Bob forms and cuts the glass and can make 48 square feet of glassper day. Each window with a wooden frame uses 6 square feet of glass and each one of aluminum, 8 square feet.

The company wants to determine how many windows of each type are necessary toproduce per day to maximize the total profit.

a) Formulate a Linear Programming model.
b) Use the graphical approach to solve the model.
c) A new rival firm in the city alsoproduces windows with wooden frames. This can force the company to lower the price and hence, the profit due to this type of windows. How would change the optimal solution (if at all) if the profitper window of wood dropped from $60 to $40? And from $60 to $20?
d) Doug is going to reduce his working hours, which would reduce the number of wooden windows produced per day. How would theoptimal solution change if there were only 5 frames daily?
ANSWERS:
(b) [pic]
(c) [pic] [pic]
(d) [pic]

3. The followingtable resumes the important facts about two products, A and B, and the resources Q, R, and S, required for their production.

Resources utilized per...