Bloomsday Outfitters produces Tshirts for road races They ne

Bloomsday Outfitters produces T-shirts for road races. They need to acquire some new stamping machines to produce 30,000 good T-shirts per month. Their plant operates 200 hours per month, but the new machines will be used for T-shirts only 60 percent of the time and the output usually includes 5 percent that are \"seconds\" and unusable. The stamping operation takes 1 minute per T-shirt, and the stamping machines are expected to have 90 percent efficiency when considering adjustments, changeover of patterns, and unavoidable downtime. How many stamping machines are required?

Solution

T shirts to be produced per month = N = 30,000

Since 5% output is unusable number of shirts to be produced = N + (5%)(N) = 30000 + (5/100)*30000 = 31500

Operating time of plant per month = T = 200 hrs

Operating time is limited to 60% so, effective operating time per month = T - (60/100)*T = 120 hrs

Now,

Since each stamping machine is 90% efficient time actually required to stamp 1 shirt will be = 1 + (1 - (90/100)*1) = 1.1 min { It takes 10% more time to stamp one shirt}

Time required to stamp 31500 shirts = 1.1min * 31500 = 34650 min = 34650/60 = 577.5 hrs

Therefore;

No. of machines required = 577.5/120 = 4.8 approximately 5 machines. { If one machine is used it can be operated for a maximum of 120 hrs per month}