A stereo manufacturer makes three types of stereo systems, I, II, and III, with profits of $20, $30, and $40, respectively. No more than 100 type-I systems can be made per day. Type-I systems require 5 man-hours, and the corresponding man-hours for types II and II are 10 and 15, respectively. If the manufacturer has available 2000 man-hours per day, determine the number of units from each system that must be manufatured in order to maximize profit. Compute the corresponding profit.
1. Type I profits $20 2. Type II profits $30 3. Type III profits $40 4. I/day < 100 5. Type I needs 5 hrs. 6. Type II needs 10 hrs. 7. Type III needs 15 hrs. 8. Total hrs. available: 2000 hrs.
Every +5 hrs. spent yields an extra $10. If we use 500 hrs. to make 100 Type I stereos, we will profit $2000. If we use 500 hrs. to make 50 Type II stereos, we will profit $1500. If we use 495 hrs. to make 33 Type III stereos, we will profit $1320.
We should use the first 500 hrs. to make Type I stereos. We should use the last 1500 hrs. to make Type II stereos.
$2000 + $4500 = x $6500 = x
There must be 100 Type I stereos made along with 150 Type II stereos made.
