A company is planning to purchase and store two items, gadgets and widgets. Each gadget costs $2.00 and occupies 2 square meters of floor space; each widget costs $3.00 and occupies 1 square meter of floor space. $1,200 is available for purchasing these items and 800 square meters of floor space is available to store them. Each gadget contributes $3.00 to profit and each widget contributes $2.00 to profit.

a) prepare out the objective profit function.
b) prepare out the constraints this company faces.
c) List all corner points and determine which combination of items will produce the maximum profit.