All-Round Bakery is a small specialty business in downtown Los Angeles that makes only two products: powdered sugar donuts and chocolate glazed donuts. Their largest customer is the LAPD, which has a daily standing order for 100 dozen sugar donuts and 100 dozen chocolate donuts. Owing to storage and supply constraints, All-Round can only stockpile enough ingredients for 400 doz sugar donuts and 200 doz chocolate donuts per day. All-Round's specialty machinery can bake 10 dozen donuts in a batch. The time required for a batch of sugar donuts is 10 minutes, or 1 minute per dozen. The time required for a batch of chocolate donuts is longer, owing to lower temperature. A batch of chocolate donuts requires 20 minutes, or 2 minutes per dozen. The machinery can operate a maximum of 10 hours (600 minutes) per day.
All-Round makes a profit of $1.75 on a dozen sugar donuts, and $2.00 on a dozen chocolate glaze donuts. How many dozen of each type should they bake daily, to maximize their profit?