For each of the problems below, write out the model including $1)$ the decision variables, $2)$ the objective function, and $3)$ the constraints. Solve the models on Excel. Please upload both the excel file as well as the written out models $($which may be handwritten, typed on word, or even typed into the excel file$).$

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular $($R$)$ and diet $($D$).$ Two of her limited resources are production time $(8$ hours $=480$ minutes per day$)$ and syrup $(1$ of the ingredients$),$ limited to $675$ gallons per day. To produce a regular case requires $2$ minutes and $5$ gallons of syrup, while a diet case needs $4$ minutes and $3$ gallons of syrup. Profits for regular soft drink are $$3\mathrm{.}00$ per case and profits for diet soft drink are $$2\mathrm{.}00$ per case.

The manager wants to know how many cases of each type of soft drink to produce in order to maximize profits.