What was the major incentive that drove captains of industry to invent machines?
The major incentive for any business leader to do anything is money. The captains of industry worked to invent machines because that would make them more profitable. It would do so by allowing products to be made faster and more cheaply.
Machines are useful to business leaders because they reduce costs. Imagine, for example, a person making shirts by hand. The person has to hand cut and hand stitch the shirts. This takes a long time, which means that the worker has to be paid a relatively high wage for each shirt. In addition, the shirts cost a lot and fewer people can buy them. But then think of how things change when machines are introduced to cut and sew the shirts. One person, using a sewing machine, can sew many more shirts than the person sewing by hand. The worker does not have to be paid as much per shirt. Shirt prices can drop, more shirts can be sold, and profits can rise. This is why captains of industry wanted machinery.
The incentive, then, was the fact that machinery makes products faster and more cheaply, thus allowing the captains of industry to make more money if they invented machines.