7.2 You are a manager at a firm like Zara, one of the leaders in fast fashion. Fast-fashion companies move their designs from catwalk to stores quickly to capture current fashion trends. You are in charge of production. Amazingly, your company can design a new product and get it to your stores in seven days, so you must decide how much to produce seven days before the units are available for sale.

Once a design is produced, you must sell whatever quantity has been manufactured. The demand for your designs fluctuates unpredictably. Compared to the situation where you could adjust your production to every change in demand, your expected loss is $1.4 million. For every day by which you can reduce the lead time, your expected loss decreases by $400,000. (For example, if you can make your production decision only six days before the products appear in the stores, your expected loss becomes

$1.4 million - $400,000 = $1 million.) Trimming the first day of lead time costs $100,000, trimming the second day costs $200,000, and so on until trimming the seventh day costs

$700,000. What is the profit-maximizing reduction in your lead time?