Home Theaters

An electronics company has hired a carpenter and an electrician to install built-in home theater systems.
They pay the carpenter $25 per hour and the electrician $30 per hour.

A standard home theater reuires 1 hour of specialized electrical work that only the 
electrician can do,  
1 hour of specialized carpentry work that only the 
carpenter can do, and
1 hour of unspecialized work that either one of them can do.  
In addition to the cost of the electrician and the carpenter, other costs for each standard home theater amount to $300.
The customer pays the store $425 for a standard home theater.

A deluxe home theater reuires 1.5 hours of specialized electrical work that only the
electrician can do,  
4 hours of specialized carpentry work that only the
carpenter can do, and
1.5 hours of unspecialized work that either one of them can do.  
In addition to the cost of the electrician and the carpenter, other costs for each standard home theater amount to $500.
The customer pays the store $800 for a standard home theater.

The sales people (part of that "other cost") claim they can sell whatever mix of standard and deluxe roome is most profitable as long as they are not asked to sell more than 10 deluxe, 12 standard, and 20 total in a week.  (If they miss the target one week there's enough baclkog that the installations can still follow the optimal miz as long as the sales department gets it back in balance the next week.


Clock here for the solution with and without supplementary variab;es