B.1 Solve the following linear programming problem graphically:
Maximize profit = 4X + 6Y
Subject to= X + 2Y <= 8
5X + 4Y <= 20
X, Y > 0
B.5 Solve the following LP problem graphically: Minimize cost = 24X + 15Y
Subject to: 7X + 11Y => 77
16X + 4Y => 80
X,Y => 0
B.7 The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate and solve this LP production-mix situation, and find the best combination of air conditioners and fans that yields the highest profit.
D.1 Customers arrive at Paul Harold’s Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Paul can perform haircuts at a rate of 5 per hour, distributed exponentially.
a) Find the average number of customers waiting for haircuts.
b) Find the average number of customers in the shop.
c) Find the average time a customer waits until it is his or her turn.
d) Find the average time a customer spends in the shop.
e) Find the percentage of time that Paul is busy.
D.9 Zimmerman’s Bank is the only bank in the small town of St. Thomas. On a typical Friday, averages of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: For Problem D9, assume µ = 15.
a) The average time in the line
b) The average number in the line.
c) The average time in the system.
d) The average number in the system.
e) The probability that the bank is empty.