Solve this linear programming problem.

A bakery wants to make a valentine cake for the valentine, they want to sell the cake for 20 days. They can produce 1000cake/day, with a price $20/cake and cost $10/cake (so the profit is $10/cake). If they want, the bakery can hire one worker to increase the production, with the help of the worker they can produce another 500cake/day (so the total become 1500/day). But they need to pay the worker $2/cake. The bakery can also make an advertisement, the fixed cost of this ads is $5000, and for every increase in $100, the ads can increase production up to 180 cakes (so every +$100 in ads. bakery will have additional 180 cakes).

How can the bakery allocate the production to achieve maximal profit? (Create the LP model (objective and restrain))

And what is the profit of this bakery?