The Affect on the Supply curve because of the product prices.

We have learnt that fall in the cost of production Shifts the Supply curve to the right,, But There is also a condition which states that the Suppliers Will shift From One product to the other if the price of that product is high,,And Supply Curve will shift to the right.
My question is If the prices of the products are high then the cost of production must be high too and how does this bring and rightward shift in the Supply Curve?