PROBLEM SET $2\mathrm{.}3E$

Hi$-$V produces three types of canned juice drinks, $A,B,$ and $C,$ using fresh strawberries, grapes, and apples. The daily supply is limited to $200$ tons of strawberries, $100$ tons of grapes, and $150$ tons of apples. The cost per ton of strawberries, grapes, and apples is $$200,$ $$100,$ and $$90,$ respectively. Each ton makes $1500$ lb of strawberry juice, $1200$ lb of grape juice, and $1000$ lb of apple juice. Drink $A$ is a $1$:$1$ mix of strawberry and apple juice. Drink $B$ is $1$:$1$:$2$ mix of strawberry, grape, and apple juice. Drink $C$ is a $2$:$3$ mix of grape and apple juice. All drinks are canned in $16-$oz $(1$ lb $)$ cans. The price per can is $$1\mathrm{.}15,$$$1\mathrm{.}25,$ and $$1\mathrm{.}20$ for drinks $A,B,$ and $C.$ Determine the optimal production mix of the three drinks.