Chapter 3.2, Problem 30E

OPTIMIZING PRODUCTION OF COLD FORMULAS Beyer Pharmaceutical produces three kinds of cold formulas: Formula I, Formula II, and Formula III. It takes $2.5\text{hr}$ to produce $1000$ bottles of Formula I, $3\text{hr}$ to produce $1000$ bottles of Formula II, and $4\text{hr}$ to produce 1000 bottles of Formula III. The profits for each $1000$ bottles of Formula I, Formula II, and Formula HI are $\$180$, $\$200$, and $\$300$, respectively. For a certain production run, there are enough ingredients on hand to make at most $9000$ bottles of Formula I, $12,000$ bottles of Formula II, and $6000$ bottles of Formula III. Furthermore, the time for the production run is limited to a maximum of $70\text{hr}$ . How many bottles of each formula should be produced in this production run so that the profit is maximized?