Operations Research Answers

The Star hotel was burned down in a fire and the manager decided to accommodate the

guests in 4–person and 8-person tents. The tents were to be hired at a cost of Kshs 1,500 and

Kshs 4,500 per night respectively, the space available could accommodate at most 13 tents

and the manager had to cope with at least 64 guests.

Required

Formulate this as a linear programming model that could be used to determine the number

of tents of each type that could pull up in order to minimize the overall cost. (10 Marks

1.     The Hardrock Concrete Company has plants in three locations and is currently working on three major construction projects, each located at a different site. The shipping cost per truckload of concrete, daily plant capacities, and daily project requirements are provided in the table below.

c) The Star hotel was burned down in a fire and the manager decided to accommodate the

guests in 4–person and 8-person tents. The tents were to be hired at a cost of Kshs 1,500 and

Kshs 4,500 per night respectively, the space available could accommodate at most 13 tents

and the manager had to cope with at least 64 guests.

Required

Formulate this as a linear programming model that could be used to determine the number

of tents of each type that could pull up in order to minimize the overall cost.

A petrol pump station has two pumps. The

service times follows the exponential

distribution with a mean of 4 minutes and

cars arrive for service in a Poisson process at

the rate 10 cars per hour. Find the

probability of that a customer has to wait for

service.

<e> 3. A firm can produce a good either by (i) a labor intensive technique, using 8 units of labor and 1 unit of capital or (ii) a capital intensive technique using 1 unit of labor and 2 units of capital. The firm can arrange up to 200 units of labor and 100 units of capital. Note that the firm produce goods X and Y in process land 1 and 2 respectively. Its objective is to maximize profit by selling the good.

i) Construct the objective function and the constant inequalities.

ii) By drawing the graphs of the linear constraints, find the optimal solutions.

 iii) Find the solution using the simplex methods.

The Red Cross wants to airlift supplies into a South American country which has

experienced an earthquake. Four types of supplies, each of which would be shipped

in containers, are being considered. One container of a particular item weighs 120,

300, 250, and 500 pounds, respectively, for the four items. If the airplane to be used

has a weight capacity of 60,000 pounds and x j equals the number of containers

shipped of item j:

a) Determine the equation which ensures that the plane will be loaded to its

weight capacity.

b) If it is decided to devote this plane to one supply item only, how many

containers could be shipped of each item?

A production plant has nine departments and the present layout is shown in the following figure. A D G B E H C F I

The movement of materials between the departments is shown in the load summary table below. To From B F I A 90 D 180 200 E 90 270 H 630 Obtain a good layout considering the unit costs of movement is Rs.10 per unit distance per load for all movements.

A production plant has nine departments and the present layout is shown in the following figure. A D G B E H C F I 

The movement of materials between the departments is shown in the load summary table below. To From B F I A 90 D 180 200 E 90 270 H 630 Obtain a good layout considering the unit costs of movement is Rs.10 per unit distance per load for all movements. 

Find initial solution for the following transportation problem using Least Cost method. D1 D2 D3 D4 Availability S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Requirements 5 8 7 14 

Solve the following LP problem by graphical method: Maximise Z = 300X1 + 700X2

Subject to the constraints: X1 + 4X2 ≤ 20 2X1 + X2 ≤ 30 X1 + X2 ≤ 8 And X1, X2 ≥ 0