The Bon$-$BBQ Grill Company manufactures and sells four different types of grills: pellet, propane, electric and charcoal. The unit price and manufacturing cost for each type of grill are summarized as follows.

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Each grill goes through four operations in the manufacturing process. The hours required by each type of grill in each of these manufacturing processes are summarized as follows.

In the next production cycle there are $2,400$ hours of machine press time available, $6,000$ hours of fabrication, $3,300$ hours of assembly, and $1,500$ hours of testing capacity. Bon$-$BBQ Grill can sell everything they make and wants to be sure that they produce at least three times as many electric grills as charcoal grills.