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# ZM 9 Smith Enterprises

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### ZM 9 Smith Enterprises - Page Text Content

FC: Pricing an Item Zachary Micciche

1: Question 9: When items are priced for sale, two factors need to be considered: - As you increase the price, you receive more money for each item sold (so your profit might increase). - As you increase the price, you won't sell as many (so your profit might decrease). Combining these two factors, as the price of an item increases the profit first increases but then decreases as the price gets too high. So the graph of the profit against the price of an item has the shape of a parabola. So the rule for profit can be modeled by a quadratic rule. Suppose that Smith Enterprises invents a new kitchen gadget. Market research suggests that if the gadget is priced at \$x, then the weekly profit P(x) in thousands of dollars will be given by: P(x) = -0.25x^2 + 3x - 5. - What profit, in dollars, would Smith Enterprises make each week if they charged \$6 per gadget? - What price should Smith Enterprises charge for a gadget to obtain the highest possible weekly profit? Explain. - What then is the highest weekly profit? - What are the break-even points; that is, what price could Smith Enterprises charge to make neither a profit nor a loss?

2: What profit, in dollars, would Smith Enterprises make each week if they charged \$6 per gadget? | P(x) is the weekly profit in thousands of dollars while x is the price of an individual kitchen gadget. P(x) = -0.25x^2 + 3x - 5 P(x) = -0.25(6)^2 + 3(6) - 5 P(x) = 4 Smith Enterprises would make a weekly profit of \$4000 if they charged \$6 per gadget.

3: What price should Smith Enterprises charge for a gadget to obtain the highest possible weekly profit? Explain. | Smith Enterprises should charge \$6 for each gadget in order to obtain the highest possible weekly profit. This is because any price below \$6 would be too cheap and Smith Enterprises would not get enough money from each purchase. Any price above \$6 would cause fewer customers to buy the product as it would be too expensive for some consumers.

4: What then is the highest weekly profit? | The highest weekly profit will be \$4000. This is because the price per gadget is \$6. When x is replaced by 6 in the equation, P(x) = 4. P(x) = -0.25x^2 + 3x - 5 P(x) = -0.25(6)^2 + 3(6) - 5 P(x) = 4 | This means that the profit is \$4000 because P(x) represents the profit in thousands of dollars. No other profit is higher than \$4000.

5: What are the break-even points; that is, what price could Smith Enterprises charge to make neither a profit nor a loss? | Smith Enterprises could price the gadgets at either \$2 or \$10 in order to break even.

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