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

A coffee firm sells "Premium blend" and "Economy blend" coffee. Both are blended

from three basic grades of coffee, A, B and C:

Premium blend = 50% A + 40% B + 10% C

Economy blend = 10% A + 40% B + 50% C

The market prices are $1130/tonne for Premium and $750/tonne for Economy. One

week the firm is given the option of buying up to 100 tonnes of grade A at $1000/tonne,

120 tonnes of grade B at $500/tonne and 100 tonnes of grade C at $300/tonne. Calculate

the profit per tonne of each blend of coffee. How much of each blend should the firm

produce to maximize its profit and what is the maximum profit?

2. Relevant equations

i know it is a linear programming problem

3. The attempt at a solution

Since i think it is a linear programming problem, i tried to solve it by using a Standard "table". so i got:

so let x1=be the number of tonnes of coffee A

x2= be the number of tonnes of coffee B

x3= be the number of tonnes of coffee C

then, Z= x1 + 0.5 x2 + 0.3 x3

And Z is subject to:

0.5 x1 + 0.4 x2 + 0.1 x3 >= NOT SURE HERE

0.1 x1 + 0.4 x2 + 0.5 x3 >= NOT SURE HERE

i am not sure how to continue, any help would be appreciated!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Optimization of equations

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