You are going to start a small business to sell premium cupcakes. The demand for cupcakes will depend on your selling p

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You are going to start a small business to sell premium
cupcakes. The demand for cupcakes will depend on your selling
price. If the selling price is p , then the monthly
demand for your cupcakes (in units) is:
monthly demand=50000-1500×p.
You have a budget of $25,000 for production cost to start up
your business in the first month. Due to economy of scales,
the average production cost of each cupcake decreases as production
increases. The cost of producing x cupcakes is:
cost=6x+ 15 x
You should only produce as many cupcakes as you can sell, and
you cannot sell more cupcakes than you produce. Your goal is
to maximize your revenue = monthly demand×price for the first
month.
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