A small clothing company manufactures two types of jackets. The first type of jacket requires 20 minutes of cutting time and 10 mins of sewing time. The second type requires 10 minutes of cutting and 15 minutes of sewing time. In one day, the company has a maximum of 12 hours of cutting times and 8 hours of sewing time.
If there are x and y of each type, then you need to evaluate some function of x and y, subject to the constraints
20x+10y <= 12*60
10x+15y <= 8*60
Complete the question using the above parameters.
To determine the maximum number of jackets the small clothing company can produce, we need to calculate the number of jackets that can be produced within the given time constraints.
First, let's convert the given hours into minutes. Since there are 60 minutes in an hour, 12 hours of cutting time is equal to 12 * 60 = 720 minutes, and 8 hours of sewing time is equal to 8 * 60 = 480 minutes.
Now, let's find out how many jackets of each type can be produced within the specified time limits.
For the first type of jacket:
- It requires 20 minutes of cutting time and 10 minutes of sewing time.
- The company has a maximum of 720 minutes of cutting time available.
- Therefore, the maximum number of jackets that can be cut for the first type is 720 minutes / 20 minutes per jacket = 36 jackets.
- Similarly, the company has 480 minutes of sewing time, so the maximum number of jackets that can be sewn for the first type is 480 minutes / 10 minutes per jacket = 48 jackets.
For the second type of jacket:
- It requires 10 minutes of cutting time and 15 minutes of sewing time.
- The company has a maximum of 720 minutes of cutting time available.
- Therefore, the maximum number of jackets that can be cut for the second type is 720 minutes / 10 minutes per jacket = 72 jackets.
- The company has 480 minutes of sewing time, so the maximum number of jackets that can be sewn for the second type is 480 minutes / 15 minutes per jacket = 32 jackets.
Now, we need to determine the minimum number of jackets the company can produce based on the limiting factor between cutting and sewing. Since the company can cut 36 jackets of the first type and 72 jackets of the second type, but can only sew 32 jackets of the second type, the sewing process becomes the limiting factor.
Hence, the maximum number of jackets the small clothing company can manufacture is 32 jackets.