Question

A t-shirt company is planning a production run for an event where the attendance (and thus demand for t-shirts) is uncertain. The event planners have indicated that they think the attendance will be 500, 750 or 1000, with probabilities of 30%, 50% and 20% respectively. The company must pre-order the blank t-shirts (cost=$5 per shirt) and it can sell finished shirts for $12 apiece. Any finished shirts that cannot be sold at the event can be sold for $2 apiece to a used clothing vendor.

Suppose now that blank t-shirts can only be ordered from the wholesale vendor in batches of 50? How many t-shirts should the company order?

Answer 1

As the question doesn't specify that what will the company do if the finished shirts are less than the actual attendance, we will be finding the probable attendance first, and then we will calculate the probable number of Blank T-shirts to be ordered.

Likely Attendance (a)	Probability (b)	Blank T-shirts to be ordered (a*b)
500	30%	150
750	50%	375
1000	20%	200
Blank T-shirts to be ordered	TOTAL	725

We find that probable attendance, and hence the requirement will be 725 T-shirts. So, The company should order at least 725 T-shirts.

But, the order quantity has to be in multiples of 50.

This means that 750 T-shirts are to be ordered.

Further, as the question doesnot specify the costs incurred by the company to convert the blank T-shirts into Finished shirts, we will not be able to calculate the profits in each Scenario.

However, the revenues to the company in each case can be calculated using the below mentioned formula.

Revenues = 12 X + 2(750 - X) .....where X is the actual attendance on the event day

For calculating profits,

Profits = Total revenues - Total Costs

= [12 X + 2(750 - X) ] - [750 (5+Y)] .....where Y is the costs of converting blank T-shirts to Finished Goods

Profits = [12 X + 2(750 - X) ] - 3750 - 750 Y

Due to inadequate information, we cannot calculate the order quantity at which Contribution/ profits are maximum.