Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 139: 116

More than 6250 tapes.

Step 1. Assume the number of tapes needed is $x$. The cost would be $10000+0.4x$ and the income would be $2x$. Step 2. To make a profit, we have $2x\gt10000+0.4x$, which gives $1.6x\gt10000$ and $x\gt6250$. Thus, more than 6250 tapes are needed to make a profit.