Operations Research Answers

Directions: Establish the table of information and formulate the LP Model of the following:

1.) Rina needs at least 48 units of protein, 60 units of carbohydrates, and 50 units of fat each month. From each kilogram of food A, she receives 2 units of protein, 4 units of carbohydrates, and 5 units of fats. Food b contains 3 units of protein, 3 units of carbohydrates, and 2 units of fats. If food A costs Php110 per kilogram and food B costs Php 90 per kilogram. How many kilograms of each food should Sofia buy each month to keep costs at a minimum?

Solve using algebraic method

z = 3000x + 5000y

2x + y <= 16

x + 2y <= 11

x + 3y <= 15

Solve using simplex method

z = 3000x + 5000y

2x + y <= 16

x + 2y <= 11

x + 3y <= 15

A bank has one drive-in counter. It is estimated that cars arrive according to Poisson distribution at

the rate of 2 every 5 minutes and that there is enough space to accommodate a line of 10 cars. Other

arriving cars can wait outside this space, if necessary. It takes 1.5 minutes on an average to serve a

customer, but the service time actually varies according to an exponential distribution. You are

required to find:

a) The probability of time, the facility remains idle.

b) The expected number of customers waiting but currently not being served at a particular point

of time.

c) The expected time a customer spends in the system

d) The probability that the waiting line will exceed the capacity of the space leading to the drive-

in counter

At a one man barber shop, customers arrive according to poison distribution with amean arrival rate of 5 per hour and hair cutting time was exponentially distributedwith an average hair cutting time was exponentially distributed with an average haircut taking 10 minutes. It is assumed that because of excellent reputation, customerswere always willing to wait. Calculate the followinga. Average number of customers in the shop and average numbers waiting for a haircutb .Percentage of time arrival can walk in right without having to waitc. The percentage of customers who have to wait before getting into the barber’s chair

Describe how you would conduct Hypothesis testing in detail. Include the information that you need in order to conduct the hypothesis test and give as many examples of the different situations/questions you can have.

Operations Research approach is

A business executive has the option of investing money in two plans. Plan A guarantees that each dollar invested will earn 70 cents a year hence, and plan B guarantees that each dollar invested will earn $2 two years hence. Plan A allows yearly

investments, while in plan B, only investments for periods that are multiples of two

years are allowed. How should the executive invest $100,000 to maximize the earnings at the end of three years? Formulate this problem as a linear programming

problem

A company's cost is sh.25 and the holding cost is 19% of average inventory. Given that the total cost is she.750, find the demand.

A plant that produces margarine has two machines that can press canola seed into

an oil. The two machines together must produce at least 900 litres of oil per day.

Machine A produces at least twice as much oil as machine B at all times. The other

processes involved in the factory stipulate that the two machines can produce a

maximum of 1500 litres of oil per day. The production cost per litre of oil of the two machines A and B is in the ratio 2: 3.

Determine the number of litres of oil that is pressed by the respective machines if the

cost is a maximum and the cost is a minimum.