5. Sand is being poured at a rate of 15 in/sec forming an expanding pile. At...

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5. Sand is being poured at a rate of 15 in/sec forming an expanding pile. At every instant, the pile of sand is in the shape a cone with equal diameter and height. How fast is the height of the pile increasing at the moment when the pile is 3 in tall? [Hint: the volume V of a cone is V = where r is the radius of the circular base of the cone and h is the height of the cone] 6. You are selling a product that costs $2 per unit to make and you can make as many units as you want. However, marketing research tells you that if you try to sell the product for $10 per unit, no one will buy the product. But if you sell it for $9 per unit, you can make 500 sales; if sell it for $8 per unit, you can make 1000 sales; if you sell it for $7 per unit, you can make 1500 sells, etc. (the number of sales goes up by 500 units for every dollar you reduce the price). Your job is to figure out the price you will charge per unit that will allow you to maximize your profit. The price should be given down to the cent. 5. Sand is being poured at a rate of 15 in/sec forming an expanding pile. At every instant, the pile of sand is in the shape a cone with equal diameter and height. How fast is the height of the pile increasing at the moment when the pile is 3 in tall? [Hint: the volume V of a cone is V = where r is the radius of the circular base of the cone and h is the height of the cone] 6. You are selling a product that costs $2 per unit to make and you can make as many units as you want. However, marketing research tells you that if you try to sell the product for $10 per unit, no one will buy the product. But if you sell it for $9 per unit, you can make 500 sales; if sell it for $8 per unit, you can make 1000 sales; if you sell it for $7 per unit, you can make 1500 sells, etc. (the number of sales goes up by 500 units for every dollar you reduce the price). Your job is to figure out the price you will charge per unit that will allow you to maximize your profit. The price should be given down to the cent.