Question $20$

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. 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. What are the optimal daily production quantities of eqach product and the optimal daily profit?

$R=40,D=100,Z=$$$320$

$R=75,D=90,Z=$$$405$

$R=90,D=75,Z=$$$420$

$R=135,D=0,Z=$$$405$