In Exercises 29 through 35, assume that the required extreme value is a relative extremum.

The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its largest commercial customers. It is estimated that if the first type of system is priced at x hundred dollars per system and the second type at y hundred dollars per system, approximately 40 − 8x + 5y consumers will buy the first type and 50 + 9x − 7y will buy the second type. If the cost of manufacturing the first type is $1,000 per system and the cost of manufacturing the second type is $3,000 per system, how should the telephone company price the systems to generate the largest possible profit?