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Applications of the Derivative in Business and Economics

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A company estimates that it can sell 6000 units each week of its product if it prices each unit at $25. However, its weekly number of sales will increase by 100 units for each 0.10 decrease in price. The company has fixed costs of $2000. The cost to make each unit is $1.80. Find the level of production that maximizes the company's profit if the company must produce and sell between and including 5000 and 17000. What is the maximum profit? The max profit is S at units. A retailer anticipates selling 7400 units of its product at a uniform rate over the next year. Each time the retailer places an order for z units, it is charged a flat fee of $100. Carrying costs are $37 per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost? They should order times a year. The minimum inventory cost is $ A retailer anticipates selling 5100 units of its product at a uniform rate over the next year. Each time the retailer places an order for a units, t is charged a flat fee of $75. Carrying costs are $34 per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost? Use the formula EOQ to obtain your answers. They should orderstimes a year. units The minimum inventory cost is $