Linear Programming

 Linear Programming Essay

PROBLEM BEST

A farmer can herb up to almost eight acres of land with

wheat and barley. He can earn $5, 000 for each and every

acre this individual plants with wheat and $3, 1000 for every

acre he crops with barley. His usage of a

important pesticide is limited by federal government

regulations to 10 gallons for his entire almost eight acres.

Whole wheat requires 2 gallons of pesticide for every

acre grown and barley requires only 1 gallon

per acerbo.

What is the utmost profit he can make?

WAY TO PROBLEM NUMBER 1

let by = the number of acres of wheat

let y sama dengan the number of massive areas of barley.

since the character earns $5, 000 for each and every acre of wheat and $3, 1000 for each corrosivo of barley, then the total profit the farmer may earn is 5000*x + 3000*y.

let p = total earnings that can be attained. your equation for revenue becomes:

s = 5000x + 3000y

that's the objective function. it's what you would like to maximize

the constraints happen to be:

number of massive areas has to be greater than or equal to 0.

range of acres needs to be less than or perhaps equal to almost eight.

amount of pesticide has to be less than or equal to 10.

your restriction equations are:

x > = 0

y > = 0

x + y = 0

con point (5, 0) may be the intersection with the line con = 15 - two times with the x-axis. the point (2, 6) is definitely the intersection of the line con = 8 - back button with the range y = 10 -- 2x.

the purpose (2, 6) was solved for inside the following method:

equations from the intersecting lines are:

y = almost eight - times

y sama dengan 10 -- 2x

take away the initial equation from your second equation and you receive: 0 = 2 - x

put x to both sides on this equation and also you get:

back button = a couple of

substitute a couple of for times in both equation to get con = 6.

that makes the intersection stage (x, y) = (2, 6).

the objective equation can be:

p = 5000x & 3000y

profit will be optimum at the intersection points of the region of feasibility on the chart. the profit formula is examined at each of such points while shown in the following desk. intersection level of (x, y) s

(0, 0) $0

(0, 8) $24, 000

(2, 6) $28, 000 *****

(5, 0) $25, 000

the maximum earnings occurs when the player plants 2 acres of wheat and 6 acres of barley. number of miles of wheat or grain is two and number of acres of barley is 6 for the total of 8 massive areas which is the maximum number of miles available for planting. number of gallons of pesticide used for whole wheat is 4 and range of gallons of pesticide intended for barley is definitely 6 for the total of 10 gallons of pesticide which is the most amount of pesticide you can use.

SOLUTION TO PROBLEM NUMBER 2

the objective function is to determine the utmost number of gallons he can mixture.

the colors engaged are color A and color M.

let x = the number of gallons of color A.

let con = the quantity of gallons of color N.

if we permit g = the maximum gallons the artist can make, then this objective function becomes:

g = times + y

make a table for color A and color B to look for the amount of every dye essential. your...