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Groovy Ukuleles

In my business, Groovy Ukuleles, I will make and sell ukuleles. My 2 types of ukuleles will be laminate and solid wood.

Business Restrictions: I won't be able to produce more than 20 solid wood ukuleles per month and no more than 35 laminate ukuleles per month. In my startup phase I can't spend more than \$4000 and I cannot spend more than \$7500 total on one product.

Business Plan: Costs and Selling prices- The solid wood ukulele will cost \$110 to produce and the laminate ukulele will cost \$50 to produce. I can sell the solid wood ukulele for \$200 and the laminate ukulele for \$100.

Restrictions: Systems of Inequalities: x=# of solid wood ukuleles y=# of laminate ukuleles

0≤x≤20

0≤y≤35

110x + 50y ≤ 4000

110x ≤ 7500

50y ≤ 7500

Business Plan: Profit- My profits will be the money made at my selling price minus the costs. x=# solid wood ukulele    y=# laminate ukuleles

Cost= 110x+50y

Sell= 200x + 100y

Profit= Sell - Cost

P= (200x+100y) - (110x + 50y) or P= 90x+50y

(20,35)

P= 90(20) + 50(35)

P= \$3550

(20,0)

P= 90(20) + 50(0)

P= \$1800

(0,35)

P= 90(0) + 50(35)

P= \$1750

To maximize my profits I would need to make 20 solid wood ukuleles and 35 laminate ukuleles.