Is this an example of horizontal integration, vertical integration, low-cost strategy, global strategy, or diversification strategy? PepsiCo purchased...

Because Pepsi
bought a company that exists further along its supply chain, this is clearly vertical
integration. That is, Pepsi bought a company that it could supply directly with Pepsi products.
We can think of Pepsi's supply and distribution chain as a vertical series of companies: all of
the companies Pepsi sources materials from that it uses in production along with all of the
companies that distribute and sell Pepsi products. Expansion in either direction along this
chain is vertical integration, whereas horizontal integration would be buying up competitorsin
this case, other companies that produce sodas, sports drinks, and the other goods Pepsi
produces.

If the question did not include the specification that Pepsi bought
KFC "so it could replace Coke products with Pepsi products in KFC restaurants," then
diversification strategy would also be a reasonable answer, since buying KFC does represent
Pepsi moving into the fast food industry, which is a form of diversification.