= 2 Problem 2. (20 points) Suppose the marginal profit P'(x) when x items are produced and sold each year is given by P'(x) = 2V - 7 measured in dollars per item. Suppose the fixed costs (that is, the cost of making 0 items is $300. (a) What is the relationship between revenue, cost, and profit? Write down an initial condition that, together with the given differential equation, creates an initial value problem (IVP) for the function P(x). (Hint: What is the revenue when no items are produced?) (b) Write down an accumulation function plus the right constant that represents the profit when producing x items. That is, write down an accumulation function plus a specific constant that is the solution of your IVP in part (a). Don't evaluate the accumulation function. (c) How many items must you sell to maximize your profit? (d) Give a formula for P(x), the yearly profit from the sale of x units and give the value of the maximum profit. (If you like, now is the time to evaluate your accumulation function). 7 = 2 Problem 2. (20 points) Suppose the marginal profit P'(x) when x items are produced and sold each year is given by P'(x) = 2V - 7 measured in dollars per item. Suppose the fixed costs (that is, the cost of making 0 items is $300. (a) What is the relationship between revenue, cost, and profit? Write down an initial condition that, together with the given differential equation, creates an initial value problem (IVP) for the function P(x). (Hint: What is the revenue when no items are produced?) (b) Write down an accumulation function plus the right constant that represents the profit when producing x items. That is, write down an accumulation function plus a specific constant that is the solution of your IVP in part (a). Don't evaluate the accumulation function. (c) How many items must you sell to maximize your profit? (d) Give a formula for P(x), the yearly profit from the sale of x units and give the value of the maximum profit. (If you like, now is the time to evaluate your accumulation function). 7