Everything Good in Life: A Roastery

Rachel Young
Friday, May 2, 2014

About

My business is a business that offers 2 types of coffee.  We offer a light roast and a dark roast

Restrictions

My business can only roast and package a total of 5000 lb. of coffee per month.  I can only spend $5500 per month on making coffee.  It costs $5 to make one pound of light roast coffee.  It costs $7 to make one pound of dark roast coffee.  To buy the coffee, it is $10 for 1 pound of light roast, and $14 for dark roast.  My company must make $6000

Systems of Equations

x = Pounds of Light Roast

y = Pounds of Dark Roast

Sell

10x+14y = S

Cost

5x+7y = C

Profit

15x+7y = P

Restrictions

x+y ≤ 500

5x+7y ≤ 500

5x+7y ≥ 300

Profit

5x+7y=P

Vertices of Feasible Region:

1. (0,71) 2. (100,0) 3. (0,43) 4. (60,0)

1. 5(0)+7(71)=$497

2. 5(100)+7(0)=$500

3. 5(0)+7(43)=$301

4. 5(60)+7(0)=$300

Conclusion

In order to maximize profit, I need to make & sell 100 pounds of light roast coffee.

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