SOLUTION: Ok this is what I think the following question is asking So the question reads: a company produces three different products: basic, mid-range, and superior. � For each basic

Question 35180: Ok this is what I think the following question is asking
So the question reads:
a company produces three different products: basic, mid-range, and superior.
� For each basic item, the company spends, on the average, $50 for the components, $20 for assembly, and $30 for packaging and dispatch.
� For a mid-range item, the spending is $100 for the components, $40 for assembly and $80 for packaging and dispatch.
� For the deluxe model, they spend $200 on components, $120 for assembly and $240 for packaging and dispatch.
If the budget allows $2,350,000 for components, $1,100,000 for assembly, and $2,050,000 for packaging and dispatch, set up and solve a system of linear equations to determine how many items of each kind can be produced.
So is what I have below on the right track or have I totally got it wrong? And what has to be done to solve it???
And the lines are supposed to be in line
.....................|Basic | Mid | Superior | Budget
Components..| 50 | 100 | 200 | 2,350,000
Assembly......| 20 | 40 | 120 | 1,100,000
Pack & disp..| 30 | 80 | 240 | 2,050,000

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
.....................|Basic | Mid | Superior | Budget
Components..| 50 | 100 | 200 | 2,350,000
Assembly......| 20 | 40 | 120 | 1,100,000
Pack & disp..| 30 | 80 | 240 | 2,050,000

So, now you have three equations in three unknows.
Do some reduction on each equation to get:
a+2b+4c=47000
a+2b+6c=55000
3a+8b+24c=205,000
Solve this system any way you know how.
I did it with a calculator using matrices to get
a=15000 (# of basic)
b=8000 (# of mid)
c=4000 (# of superior)
Cheers,
Stan H.
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