MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $5800 per month. Materials and labor for each helmet of this model are $40, and the company sells this helmet to dealers for $65 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) - (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) - (d) Find C(200) C(200) - Interpret C(200) For each $1 increase in cost this many more helmets can be produced. This is the cost (in dollars) of producing 200 helmets. When this many helmets are produced the cost is $200. For every additional helmet produced the cost increases by this much. Find R(200) R(200) - Interpret R(200) O When this many helmets are produced the revenue generated is $200. This is the revenue (in dollars) generated from the sale of 200 helmets. For each $1 increase in revenue this many more helmets can be produced. For every additional helmet produced the revenue generated increases by this much Find P(200) PX200) = Interpret P200). This is the profit (in dollars) when 200 helmets are sold, but since it is negative it means that the company loses money when 200 helmets are sold. This is the profit (in dollars) when 200 helmets are sold, and since it is positive it means that the company makes money when 200 helmets are sold For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets. For each additional helmet sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of helmets sold in order to make a profit. (e) Find C(300) C(300) - Interpret C(300). For each $1 increase in cost this many more helmets can be produced For every additional helmet produced the cost increases by this much When this many helmets are produced the cost is $300. This is the cost (in dollars) of producing 300 helmets. Find R(300) R(300) - Interpret R(300) For each $1 increase in revenue this many more helmets can be produced, When this many helmets are produced the revenue generated is $300 This is the revenue (in dollars) generated from the sale of 300 helmets. For every additional helmet produced the revenue generated increases by this much Find P300), P(300) - Interpret P(300). This is the profit (in dollars) when 300 helmets are sold, and since it is positive it means that the company makes money when 300 helmets are sold. For each additional helmet sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of helmets sold in order to make a profit. This is the profit (in dollars) when 300 helmets are sold, but since it is negative it means that the company loses money when 300 helmets are sold. For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets. (1) Find the marginal profit MP. MP - Write a sentence that explains its meaning. O When costs are decreased by this much the profit is increased by $1. For each $1 increase in profit this many more helmets can be produced, Each additional helmet sold increases the profit by this many dollars. When revenue is increased by this much the profit is increased by $1