Dwight and Hattie have run the family farm for over thirty years.They are currently planning the mix of crops to plant on their 120-acre farm for the upcoming season.The table below gives the labor hours and fertilizer required per acre,as well as the total expected profit per acre for each of the potential crops under consideration.Dwight,Hattie,and their children can work at most 6,500 total hours during the upcoming season.They have 200 tons of fertilizer available.What mix of crops should be planted to maximize the family's total profit? 
(a)Formulate and solve a linear programming model for this problem in a spreadsheet.(b)Formulate this same model algebraically.
Definitions:
Quartz
A hard, crystalline mineral composed of silicon dioxide, notable for its durability and its use in making jewelry and electronic equipment.
Oxides
Compounds composed of oxygen and another element, which can form minerals and play significant roles in geological processes.
Hematite
Hematite is an iron oxide mineral and one of the main iron ores, characterized by its reddish-black color, metallic or earthy luster, and used as an important source of iron.
Element O
Element O refers to Oxygen, a chemical element with the symbol O and atomic number 8, essential for life and a major part of the Earth's atmosphere.
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