Question

# A company makes four types of gourmet chocolate bars. Chocolate Bar I contains 5 grams...

A company makes four types of gourmet chocolate bars. Chocolate Bar I contains 5 grams of nuts, 5 grams of biscuit, 10 grams of caramel, and 100 grams of chocolate, and sells for \$5.40. Chocolate Bar II contains 10 grams of nuts, 10 grams of biscuit, 10 grams of caramel, and 90 grams of chocolate and sells for \$6.25. Chocolate Bar III contains no nuts, 10 grams of biscuit, 10 grams of caramel, and 100 grams of chocolate and sells for \$5.25. Chocolate Bar IV contains 20 grams of nuts, no biscuit, 10 grams of caramel, and 90 grams of chocolate and sells for \$7.00. The ingredient costs are \$0.15 per gram of nuts, \$0.025 per gram of biscuit, \$0.02 per gram of caramel, and \$0.015 per gram of chocolate. The company has supplier agreements that force them to order at least 50,000 grams of each ingredient per week (nuts, biscuit, caramel, and chocolate). However, due to the space in their warehouse and the expense of holding too much inventory, the company cannot hold more than 100,000 grams of nuts; 75,000 grams of biscuits; 85,000 grams of caramel; and 500,000 grams of chocolate per week. How many chocolate bars of each type should the company produce each week in order to maximize its weekly profit?

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