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 occu pies 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) Write out the objecti ve profit function. b) Write out the constraints this company faces. c) Calculate (with details) and list all corner points and determine which combination of items will produce the maximum profit.