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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.

Sagot :

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So,

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.
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