Advanced Algebra II Notes 6.6 Linear Programming The Elite Pottery Shoppe makes two kinds of birdbaths: a fancy glazed and a simple unglazed. An unglazed birdbath requires .5 h to make using a pottery wheel and 3 h in the kiln. A glazed birdbath takes 1 h on the wheel and 18 h in the kiln. The company’s one pottery wheel is available for at most 8 hours per day (h/d). The three kilns can be used a total of at most 60 h/d. The company has a standing order for 6 unglazed birdbaths per day, so it must produce at least that may. The pottery shop’s profit on each unglazed birdbath is $10, and the profit on each glazed birdbath is $40. How many of each kind of birdbath should the company produce each day in order to maximize profit?

Amount per unglazed Birdbath Amount per glazed Constraining value Wheel hours Kiln hours Profit

Profit equation: _____________________________   Constraint inequalities: _______________________________ _______________________________ Vertices of feasible region: _________________________________________

Marco is planning a snack of graham crackers and blueberry yogurt to provide at his school’s track practice. Because he is concerned about health and nutrition, he wants to make sure that the snack contains no more than 700 calories and no more than 20 g of fat. He also wants at least 17 g of protein and at least 30% of the daily recommended value of iron. The nutritional content of each food is listed in the table below. Each serving of yogurt costs $0.30 and each graham cracker costs $0.06. What combination of servings of graham crackers and blueberry yogurt should Marco provide to minimize cost? Serving Calories Fat Protein Iron (percent of daily Recommended value) Graham crackers 1 cracker 60 2 g 6% Blueberry yogurt 4.5 oz 130 5 g 1 %

Amount per graham cracker Amount per serving of yogurt Limiting value Calories Fat Protein Iron Cost

Cost equation: _____________________________ Constraint inequalities: _______________________________ _______________________________ ________________________________   Vertices of feasible region: _________________________________________

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