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# Ryan's Records

Ryan Dowdy - April 21, 2015

Ryan's Records is a business based around selling record players and vinyl records of diverse genres. Ryan's Records will stay up to date with it's collection of vinyls to sell and produce it's own record players to sell.

# Costs to Produce

Producing one record player will cost Ryan's Records \$40, and buying vinyls to sell will cost \$10 per vinyl.

# Profit from Sales

Each record player produced by Ryan's Records can be sold for \$100, and each vinyl can be sold for \$20.

Therefore, Each record player sold will result in \$60 profit, and each Vinyl will result in \$10 profit.

# Restrictions

With a starting budget of \$10,000 to produce my product, I do not want to spend more than \$2000 in the first month.

40x + 10y <= 2000

Because the vinyls are bought in bulk to help reduce costs, I can not purchase less than 100 vinyls to sell at my store each month.

y >= 100

On average, Each customer that purchases a record player will also purchase at least 3 new records to play on their new record player. Therefore, my number of records should be a minimum of 3 times greater than the number of record players produced.

x <= 3y

I can not reasonably sell more than 50 record players in a month, so it would be unreasonable to produce more than that.

x <= 50

# Maximize Profits

Profit = 60x + 10y

(0, 100) 60(0) + 10(100) = \$1000

(25, 100) 60(25) + 10(100) = \$2500

(0, 200) 60(0) + 10(200) = \$2000

My profit will be maximized if I produce 25 record players, and purchase 100 records each month.