What is the role of system of linear equation and matrices in business?

Question

Can anyone tell me what is the role of system of linear equation and matrices in business with one example

Answer 1

One is Inventory system models. Ok, suppose you wanna order two products, A and B. The cost of A is 10 cents each. Cost of B, 20 cents. The money you got to spend is, say, 5 dollars. So first linear equation:

10X + 20Y= 500 or 1X+2Y=50

Where X and Y represent how MANY each you order. Now suppose you have 90 square feet of space in yer storage for them. Each A takes up 2 square feet, and each B takes up 1 square foot.

Second equation (assuming you must fill up all the space or close to it):

2X+1Y=90

Where X,Y are non-negative.

matrix
[ 01 02 050 ]
[ 02 01 090 ]

Solution Y= 3 , X= 43 (approximately ... can't have fractions). Represents the intersection of two lines.

Often you will have another equation that you must maximize (profit), and that equation would include sales. Maximize profit is the role. These two equations would then be conditions. Costs to include could be transportation, say. Maintenance. Whatever.

Answer 2

i will think of of a minimum of four procedures: a million) removing (upload or subtract the equations to get rid of a variable) 2) substitution (rearrange one equation to get one equation by utilising itself, then substitute into the different equation 3) Kramer's Rule (matrix operations) 4) Graphically (seek for the intersection) particular, a equipment could have greater beneficial than one answer-- if the traces are each and every of a similar line, there are an infinite form of suggestions (each and every component on the line is a answer). Algebraically, you finally end up with something that sounds like 0 = 0 or 3 = 3. A equipment can even have not have been given any suggestions (if the traces are parallel, or if greater beneficial than 2 traces intersect do no longer intersect in one component). Algebraically, you finally end up with something that sounds like 0 = 3, or 9 = 12. the way the equations are offered many times determine that's way less complicated. ex: y = 3x - 5 2x + 3y = 18 ==> as a results of fact the 1st equation is already solved for y, this may be much less complicated to apply substitution (the 2nd equation might become : 2x + 3(3x - 5) = 18 4x - 5y = -8 2x + 5y = 26 ==> may be much less complicated to remedy by utilising removing, in view that including the equtions might yield 6x = 18 notice: now and returned, if the 1st answer you calculate is a "messy fraction", it would then be much less complicated to circulate returned and get rid of the different variable particularly than substitute the fraction returned in to remedy for the different despite if, carried out precise, each and every approach will yield a similar answer. Graphically (by utilising hand) is the trickiest to reach on the suited answer-- exceptionally despite if it is no longer an integer, or the coefficients at the instant are not integers. A calculator seems after this.

Answer 3

Well, one big one is supply and demand. The more you charge for something, the more money you will make if you sell one. That's a line with positive slope. However, the more you charge, the fewer people will buy one. That's a line with negative slope. Where those two lines cross is the place where you maximize profit. That's basically what business is all about.