Question

Question: Duckwheat is produced in Kansas and Mexico and consumed in New York and California. Kansas produces 15 shnupells of duckwheat and Mexico 8. Meanwhile, New York consumes 10 shnupells and California 13. The transportation costs per shnupell are \(4 from Mexico to New York, \)1 from Mexico to California, \(2 from Kansas to New York, and \)3 and from Kansas to California. Write a linear program that decides the amounts of duckwheat (in shnupells and fractions of a shnupell) to be transported from each producer to each consumer, so as to minimize the overall transportation cost

Short answer

Answer:

The minimum transportation cost: 4MN+MC+2KN+3KC.

MN+KN=10

MC+KC=13

MN+MC=8

KN+KC=15

MN≥0, MC≥0, KN≥0, KC≥0 will be therequired linear program

Step-by-step solution

Defining the variables

For our convenience, let us denote each country by its first alphabet:

M=Mexico

K=Kansas

N=New York

C=California

Let the number of shnupells shipped from Kansas to New York be “KN” and its transportation cost is $2.So, the transportation cost will become 2KN.

Let the number of shnupells shipped from Kansas to California be “KC” and its transportation cost is $3.So, the transportation cost will become 3KC.

Let the number of shnupells shipped from Mexico to New York be “MN” and its transportation cost is $4.So, the transportation cost will become 4MN.

Let the number of shnupells shipped from Mexico to California be “MC” and its transportation cost is $1.So, transportation cost will become 1MC.

Defining the constraints which will be the desired Linear Program

The constraints can be formed as follows:

The minimum transportation cost: 4MN+MC+2KN+3KC.

MN+KN=10

MC+KC=13

MN+MC=8

KN+KC=15

MN≥0, MC≥0, KN≥0, KC≥0 will be therequired linear program.