Provide a fully typed solution using strategies taught in grade 12 calculus class in high school.Thanks!

Your neighbor operates a successful bake shop. One of their specialties is a very rich, whipped- cream-covered cake. They buy the cakes from a supplier who charges $6.00 per cake, and they sell 200 cakes weekly at $10.00 each. Research shows that profit from the cake sales can be increased by increasing the price. Unfortunately, for every increase of $0.50 (every increase of 50c) , cake sales will drop by seven cakes. (5 marks) What is the optimal retail price for a cake to obtain a maximum weekly profit