Business Find expression for the revenue, cost, and profit from selling x thousand items....

Business Find expression for the revenue, cost, and profit from selling x thousand items. (See Example 11.)

Example 11

Hot Rocks Movies sells DVDs for $8 each (wholesale) and can produce a maximum of 200,000 DVDs. The variable cose of producing x thousand DVDs is 3550x − 8x2 dollars, and the fixed costs for the manufacturing operation are $215,000. If x thousand DVDs are manufactured and sold, find expressions for the revenue, cost, and profit.

Solution

If x thousand DVDs are sold at $8 each, then

where x ≤ 200 (because only 200,000 DVDs can be made). The variable cost of making x thousand DVDs is 3550x − 8x2, so that

Therefore, the profit is given by