Problem 1: Lisa Simpson sells beauty supplies. Her annual demand for a particular skin lotion is 1,000 units. The cost of placing an order is $20, while the holding cost per unit per year is 10 percent of the cost. This item currently costs $10 if the order quantity is less than 300. For orders of 300 units or more, the cost falls to $9.80. To minimize total cost, how many units should Lisa order each time she places an order? What is the minimum total cost?
Problem 2: Furniture Fanatics Inc., uses 20,000 loads of lumber per year. A load of lumber costs $500 and the carrying cost is 10 percent of the unit cost. The cost to order is $200 per order and the lead-time is three working days. Assuming 200 working days, determine:
(a) the economic order quantity.
(b) the reorder point.
(c) number of orders per year.
(d) working days between orders.
Problem 3: Annie Lennox recently took over a cleaning supply store. Her predecessor always ordered carpet shampoo in quantities of 100 units. Annie is reevaluating this policy. Based on her analysis, the cost to place each order is $35 and the holding cost is $8 per shampoo bottle per year. The annual demand for this product is 2500 bottles. Should Anne change the current order policy and, if so, how much can she save?
Problem 4: Candy Incorporated stocks bubble gum game cards, an item that has a normally distributed demand during the reorder period with a mean of 12 dozen boxes and a standard deviation of two dozen boxes. If it is desirable to experience a stock-out only 10 percent of the time, what is the appropriate safety stock?
Problem 5: Billy Idell is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the Standard model, while the other is the Deluxe model. The profit per unit on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The Standard model requires 20 minutes of assembly time, while the Deluxe model requires 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day. How many units of each product should be manufactured to maximize profits?
Problem 6: Chewy's produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.90, and each pound of grain costs $0.60. A pound of the dog food must contain at least 9 units of Vitamin 1 and 10 units of Vitamin 2. A pound of beef contains 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of grain contains 6 units of Vitamin 1 and 9 units of Vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of the final product?