roblem $1($Algebraic Form$)(30$ pts$.)$

The demand for ice cream at All$-$Flavors Parlor during the $3$ summer months $($June$,$ July, and August$)$

is estimated at $500,600,$ and $40020-$gallon cartons, respectively. Two wholesalers, A and B$,$ supply

All$-$flavors with its ice cream. The maximum number of cartons either supplier can provide is $400$ per

month. Also, the price the suppliers charge changes monthly according to the following schedule:

Price per carton in month

June July August

Supplier $1$ $$100$ $$110$ $$120$

Supplier $2$ $$115$ $$108$ $$125$

To take advantage of price fluctuation, All$-$flavors can purchase more than is needed for a month and

store the surplus to satisfy the demand in a later month. The storage cost of ice cream cartons is $$5$ per

month. Develop a linear programming model to determine the optimum schedule for buying ice cream

from the two suppliers. For full credit, build an algebraic model.