P(x)=300x - 3,300 P(343)=300343 343 - 3,300 99600 99,600 That is, if 343 items are produced and sold, the total profit is $99600 Step 4 (c) How many items must be sold to avoid losing money? 99,600 The manufacturer makes money if the profit is positive positive and loses money if the profit is negative negative When the manufacturer breaks even, the profit is So, to avoid losing money, the manufacturer must produce and sell the break-even quantity, which is the number of items that results in a profit equal to 0. We can find the break-even quantity by solving the equation P(x)=0 0 Step 5 To find the break-even quantity, substitute 300x -3,300 for P(x) in the equation P(x) = 0, and solve for x. (Since the equation is linear, isolate x on the left side of the equation.) P(x) = 0 )x-3,300 = 0 300x=>