# Operations research

Please find attached the questions.Thank you

1.

Suppose that England, France, and Spain produce all the wheat, barley, and oats in the

world. The world demand for wheat requires 125 million acres of land devoted to wheat

production. Similarly, 60 million acres of land are required for barley and 75 million

acres of land for oats. The total amount of land available for these purposes in England,

France, and Spain is 70 million acres, 110 million acres, and 80 million acres,

respectively. The number of hours of labor needed in England, France and Spain to

produce an acre of wheat is 18, 13, and 16, respectively. The number of hours of labor

needed in England, France, and Spain to produce an acre of barley is 15, 12, and 12,

respectively. The number of hours of labor needed in England, France, and Spain to

produce an acre of oats is 12, 10, and 16, respectively. The labor cost per hour in

producing wheat is $9.00, $7.20, and $9.90 in England, France, and Spain, respectively.

The labor cost per hour in producing barley is $8.10, $9.00, and $8.40 in England, France,

and Spain respectively. The labor cost per hour in producing oats is $6.90, $7.50, and

$6.30 in England, France, and Spain, respectively. The problem is to allocate land use in

each country so as to meet the world food requirement and minimize the total labor cost.

(a) Formulate this problem as a transportation problem by constructing the appropriate

parameter table.

(b) Draw the network representation of this problem.

(c) Obtain an optimal solution.

2.

Reconsider the problem in the preceding example. Starting with the northwest corner rule,

interactively apply the transportation simplex method to obtain an optimal solution for

this problem.

https://brainmass.com/math/linear-programming/operations-research-producing-wheat-361626

#### Solution Preview

1.

Suppose that England, France, and Spain produce all the wheat, barley, and oats in the

world. The world demand for wheat requires 125 million acres of land devoted to wheat

production. Similarly, 60 million acres of land are required for barley and 75 million

acres of land for oats. The total amount of land available for these purposes in England,

France, and Spain is 70 million acres, 110 million acres, and 80 million acres,

respectively. The number of hours of labor needed in England, France and Spain to

produce an acre of wheat is 18, 13, and 16, respectively. The number of hours of labor

needed in England, France, and Spain to produce an acre of barley is 15, 12, and 12,

respectively. The number of hours of labor needed in England, France, and Spain to

produce an acre of oats is 12, 10, and 16, respectively. The labor cost per hour in

producing wheat is $9.00, $7.20, and $9.90 in England, France, and Spain, respectively.

The labor cost per hour in producing barley is $8.10, $9.00, and $8.40 in England, France,

and Spain respectively. The labor cost per hour in producing oats is $6.90, $7.50, and

$6.30 in England, France, and Spain, respectively. The problem is to allocate land use in

each country so as to meet the world food requirement and minimize the total labor cost.

(a) Formulate this problem as a transportation problem by constructing the appropriate

parameter table.

(b) Draw the network representation of this problem.

(c) Obtain an optimal solution.

2.

Reconsider the problem in the preceding example. Starting with the northwest corner rule,

interactively apply the transportation simplex method to obtain an optimal solution for

this problem.

(The Actual Problem)

ANSWERS

Problem 1

(a) Formulate this problem as a transportation problem by constructing the appropriate parameter table.

We can choose England, France and Spain to be the 3 sources. We can also choose Wheat, Barley, and Oats be the three destinations. The unit cost (in millions of dollars) is the labor cost per ...

#### Solution Summary

Operations research is contemplated in this solution. Transportation problems by construction are formulated.