In the Ma-and Pa grociery stores, shelf space is limited and must be used effectively to increase profit. Two cereal items, Grano and Wheatie, compete for a total shelf space of 60 square feet. A box of Grano occupies .2 square feet and a box of Wheatie needs .4 square feet.The maximum daily demand of Grano and Wheatie are 200 and 120 boxes respectively. A box of Grano nets 1.00$ in profit and a box of Wheatie 1.35$. Ma-and -Pa thinks that because the unit profit of Wheatie is 35% higher ,Wheatie should be allocated 35% more space, which amount to allocating about 57% to Wheatie and 43% to Grano. What do you think?
a) Define decision variables; b) Define an objective function (give a mathematical expression for the objective function); c) State all constraints which apply to the problem; and d) Identify the values which the decision variables have in the optimal solution, and the value of the objective function which results when the decision variables assume their optimal values.