SOLUTION: Tremendous Enterprise produces three brands of herbal medicine:A,B and C.Each bottle of brand A requires 2ml of ingredient X,and 3ml of ingredient Y and 5ml of ingredient Z.Each bo

Question 761856: Tremendous Enterprise produces three brands of herbal medicine:A,B and C.Each bottle of brand A requires 2ml of ingredient X,and 3ml of ingredient Y and 5ml of ingredient Z.Each bottle of brand B requires 3ml of X,4ml of Y and 4ml of Z.Finally,each bottle of brand C requires 1ml of X,2ml of Y and 7ml of Z.Available are 1900ml of ingredient X,2900ml of Y and 5450ml of Z.
a) Set up this problem as a system of linear equations that can be solved to obtain the number of bottles of each brand of herbal medicine that must be produced if all the available ingredients must be used up.
b) Write the above system of linear equations in matrix form.
c) Using a matrix method,determine the number of each brand of herbal medicine that must be produced.
d) The selling prices for brands A,B and C are respectively $10,$15 and $30 per bottle,and the total production cost for the different brands of herbal medicine obtained in (c) above is $10,000.
Using your answer in (c) above,advice the Management of Tremendous Enterprise on the profitability of the venture.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Tremendous Enterprise produces three brands of herbal medicine:A,B and C.
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Each bottle of brand A requires 2ml of ingredient X,and 3ml of ingredient Y and 5ml of ingredient Z.
Each bottle of brand B requires 3ml of X,4ml of Y and 4ml of Z.
Finally,each bottle of brand C requires 1ml of X,2ml of Y and 7ml of Z
----------------------------------------
Available are 1900ml of ingredient X,2900ml of Y and 5450ml of Z.
--------------------
a) Set up this problem as a system of linear equations that can be solved to obtain the number of bottles of each brand of herbal medicine that must be produced if all the available ingredients must be used up.
----
Equations:
Ingrediant X: 2A + 3B + C = 1900
Ingrediant Y: 3A + 4B + 2C = 2900
Ingrediant Z: 5A + 4B + 7C = 5450
=====================================
Using a matrix method on my TI-84 I get:
A = 400 bottles
B = 250
C = 350
==================
Cheers,
Stan H.
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