Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 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) = ◇ 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. ◇ 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. (e) Find C(300). C(300) = Interpret C(300). When this many helmets are produced the cost is $300. This is the cost (in dollars) of producing 300 helmets. For each $1 increase in cost this many more helmets can be produced. ◇ For every additional helmet produced the cost increases by this much. (c) Write the function for profit P(x). P(x) = Find R(300). (d) Find C(200). C(200) = Interpret C(200). When this many helmets are produced the cost is $200. For every additional helmet produced the cost increases by this much. This is the cost (in dollars) of producing 200 helmets. For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) = Interpret R(200). For each $1 increase in revenue this many more helmets can be produced. ◇ This is the revenue (in dollars) generated from the sale of 200 helmets. When this many helmets are produced the revenue generated is $200. For every additional helmet produced the revenue generated increases by this much. Find P(200). P(200)= Interpret P(200). ○ 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. R(300) = Interpret R(300). ◇ When this many helmets are produced the revenue generated is $300. ◇ For every additional helmet produced the revenue generated increases by this much. For each $1 increase in revenue this many more helmets can be produced. This is the revenue (in dollars) generated from the sale of 300 helmets. Find P(300). P(300) = Interpret P(300). 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. ◇ 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, and since it is positive it means that the company makes money when 300 helmets are sold. (f) Find the marginal profit MP. MP = Write a sentence that explains its meaning. Each additional helmet sold increases the profit by this many dollars. ◇ For each $1 increase in profit this many more helmets can be produced. When costs are decreased by this much the profit is increased by $1.