Question

A company manufactures gadgets that come in small, medium, and large. The storage area can hold a total of 45 boxes. Each box can hold 200 small, 100 medium, or 50 large gadgets. They have enough hours to make 5000 gadgets. A box of small gadgets takes 2 hours to pack, while the boxes of medium or large require only 1 hour. They have 60 hours available for packing. Small gadgets sell for $30 a box, medium for $10, and large for $20. How many boxes of each should be made to maximize their revenue? Have they used all available storage room and hours? Tell the story behind each basic feasible solution. Be sure to include the slack variables and specify if this is a maximum.