A process produces two types of products A and B. Product A is done in batches of 1000 units. It involves a setup time of 2 hours and a run time of 75 seconds. Product B is done in batches of 500 units and involves a setup time of 1 hour and a run time of 45 seconds.

How many units can this process produce in a week of 40 hours, if:

only product A is produced?
only product B is produced?
A and B are produced in a mix of 25% A and 75% B?

Explanation:

1. Only product A is produced

40 hours= 40*60*60 = 144,000 seconds

Run time 75 seconds

Setup time 2 hours

Batches= 1000 units

Run time to produce one batch of A = 1000*75sec = 75,000 seconds

Setup time = 2 hours = 7200 seconds

Remaining seconds = 144,000 - (75,000+7200) = 61,800 seconds

Product A manufactured in 61,800 sec = 61,800/75 = 824

Total Product A manufactured are = 1824 units

2. Only product B is produced

40 hours= 40*60*60 = 144,000 seconds

Run time 45 seconds  

Setup time= 1 hour

Batches= 500 units

To produce one batch of A = 500*45sec = 22,500 seconds

Setup time = 6 hours = 6*7200 seconds= 43,200sec

Remaining seconds = 144,000-(22,500+43,200) = 78,300 seconds

Product A manufactured in 78300 sec = 1740

Total Product A manufactured are = 500+1740= 2240 units

3. A and B are produced in a mix of 25% A and 75% B?

Considering loss of 3 hours setup time, 37 hours is left to produce

A is manufactured for = 25% of 37 hours = 9.25 hours = 33300 hours

B is manufactured for = 75% of 37 hours = 27.75 hours = 99900 hours

Production of A = 33300/75 sec= 444 units

Production of B = 99900/45 sec= 2220 units

a. only product A is produced = 1,824 units

b. only product B is produced = 3,120 units

c. A and B are produced in a mix of 25% A and 75% B = 444 units of A, and 2,220 units of B

Explanation:

a. Only Product A is Produced

Number of hours of production per week = 40 hours

Converts this time to seconds we have

= 40 x 60 x 60 = 144,000 seconds

Setup time for Product A = 2 hours

Convert to seconds we get:

2 x 60 x 60 = 7,200 seconds

Product A is done in batches of 1000 units

Run time for Product A = 75 seconds (Time to produce a unit of Product A)

Hence time taken to produce 1000 units = 75 second x 1000 = 75,000 seconds

Hence Remaining time after producing 1000 units will be:

144,000 - (75,000 + 7,200) = 61,800 seconds

Hence the number of units that can be produced in this time, knowing that 1 unit takes 75 seconds to be produced = 61,800/75 = 824 units

Hence Total unit of Product A = 1000 + 824 = 1,824 units

b. Only product B is produced

Number of hours of production per week = 40 hours

Converts this time to seconds we have

= 40 x 60 x 60 = 144,000 seconds

Setup time for Product B = 1 hours

Convert to seconds we get:

1 x 60 x 60 = 3,600 seconds

Product B is done in batches of 500 units

Run time for Product B = 45 seconds (Time to produce a unit of Product A)

Hence time taken to produce 500 units = 45 second x 500 = 22,500 seconds

Hence Remaining time after producing 500 units of Product B will be:

144,000 - (22,500 + 3,600) = 117,900 seconds

Hence the number of units that can be produced in this time, knowing that 1 unit takes 45 seconds to be produced = 117,900/45 = 2,620 units

Hence Total unit of Product B = 500 + 2,620 = 3,120 units

c. A and B are produced in a mix of 25% A and 75% B

Setup time for Product A = 2 hrs

Set up time for Product B = 1 hr

Total setup time = 3 hours

Number of hours of production = 40 hours

Number of hours of production barring loss time = 40 hours - 3 hours = 37 hours

25% of Product A will use 25% of time, which is:

0.25 x 37 = 9.25 hours = 9.25 x 60 x 60 = 33,300 seconds

75% of Product B will use 75% of the useful time, which is:

0.75 x 37 = 27.75 hours = 27.75 x 60 x 60 = 99,900 seconds

Product A run time is 75 seconds, Hence total product in the time allocated:

= 33,300/75 = 444 units of Product A

Product A run time is 45 seconds, Hence total product in the time allocated:

= 99,900/45 = 2,220 units

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