Question

Question 1 )

From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 8 cars per hour all day Saturday. With a crew working the wash line, harry figures that car can be cleaned at the rate of one every 6 minutes. One car at a time cleaned in this example of a single-channel waiting line. Assuming Poisson arrival and exponential service times, find the

1- Average number of cars in line.

2- Average time a car waits before it is washed.

3- Average time a car spends in the service system.

4- Utilization rate of the car wash.

5 - Probability that no car are in the system.

Question 2 )

Woofer Pet Food produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.80, and each pound of grain costs $0.50. A pound of the dog food must contain at least 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of beef contains 5 units of vitamin 1 and 7 units of vitamin 2. A pound of grain contains 6 units of vitamin 1 and 9 unites of vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of final product?

From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 8 cars per hour all day Saturday. With a crew working the wash line, harry figures that car can be cleaned at the rate of one every 6 minutes. One car at a time cleaned in this example of a single-channel waiting line. Assuming Poisson arrival and exponential service times, find the

Average number of cars in line.

Average time a car waits before it is washed.

Average time a car spends in the service system.

Utilization rate of the car wash.

Probability that no car are in the system.

Woofer Pet Food produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.80, and each pound of grain costs $0.50. A pound of the dog food must contain at least 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of beef contains 5 units of vitamin 1 and 7 units of vitamin 2. A pound of grain contains 6 units of vitamin 1 and 9 unites of vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of final product?

Answer 1