(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A fertiliser company sells four types of lawn fertiliser.

Brand A 24-4-8, Brand B 21-7-12, Brand C 17-0-0 , Brand D 0-12-12. The three

numbers refers to the percentage of nitrogen, phosphate and potassium in that order

contained in each brand. Suppose that each year your lawn requires 500g of nitrogen,

100g of phosphate and 180g of potassium. You want to find the amount of each of

the four brands of fertiliser that is required to do this.

(a) Set up this information as a matrix equation with the coefficient matrix

of size 3x4.

(b) Using row transformations solve for the amount of each brand of fertiliser.

(c) Find the exact amount for each brand when you use

(i) the minimum amount of Brand D allowed

(ii) the maximum amount of brand D allowed

2. Relevant equations

3. The attempt at a solution

I'm having trouble working out how to attach this. We've only really solved for unknowns with neat square matrices before.

a)

I throw it together in a matrix like this:

24, 21, 17, 0 : 500

4, 7, 0, 12 : 100

8, 12, 0, 12: 180

But then i don't know what to do, because the # of unknowns is more than the # of equations.

Any help?

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# Homework Help: Matrix Question

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