Rocky Mountain Coffee

In my business "Rocky Mountain Coffee" I will be selling salted caramel pretzel frappucino and vanilla bean harvest frappuccino dry mixes. These mixes to be bought ahead of time so you can have your favorite Rocky Mountain Coffee without even leaving the house.  

Restrictions:

I won't be able to produce more than 100 mixes of the Salted caramel pretzel mix and no more than 200 mixes. In my start up phase, I can't spend more than $800 each month. I also cannot spend more than $7500 total on any one product.

Costs and Selling Prices:

The salted caramel pretzel frappuccino will cost $6 to produce and the Vanilla Bean Harvest frappuccino mix costs $3 t0 produce.

I can sell the Salted Caramel Pretzel frappuccino mix $15.50 and $12 for the Vanilla Bean Harvest frappuccino mix.

Systems of Inequalities:

x = # of Salted Caramel Pretzel Frappuccino mix

y = # of Vanilla Bean Harvest Frappuccino mix

6x+3y < 800

6x<7500

3y<7500

0<x<100

0<y<200

Profits:

My profits will be the money made at my selling price minus the costs.

x= # of Salted Caramel Pretzel   y = # of Vanilla Bean Harvest

Production Cost = 6x+4y

Sell Price = 15.5x+12y

Maximize Profits:

(0, 200) P = 9.5 (0) + 8 (200) = $1,600

(33.3,200) P = 9.5 (33.3) + 8 (200) = $1916.35

[Since you can't sell a third of something.... P = 9.5 (33) + 8 (200) = $1913.5]

(100,66.7) P = 9.5 (100) + 8 (66.7) = $1483.6

(100,0) P = 9.5 (1oo) + 8 (0) = $950

(0,0) P = 9.5 (0) + 8 (0) = $0

I will maximize my profits each month if I produce 33 bags of Salted Caramel Pretzel mix and 200 bags of Vanilla Bean Harvest mix.

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