2. 外语
  3. To produce a particular radio model, it costs a manufacturer $30 per radio, and it is assumed that if 500 radios are produced, a

To produce a particular radio model, it costs a manufacturer $30 per radio, and it is assumed that if 500 radios are produced, a

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问题 To produce a particular radio model, it costs a manufacturer $30 per radio, and it is assumed that if 500 radios are produced, all of them will be sold. What must be the selling price per radio to ensure that the profit(revenue from the sales minus the total production cost)on the 500 radios is greater than $8,200?
选项
答案$46.40
解析 If y represents the selling price per radio, then the profit is 500(y - 30). Therefore, we set
500(y-30)> 8,200
Solving the inequality, we get
500y- 15,000 > 8,200
500y> 23,200
y > 46.4
Thus, the selling price must be greater than $46.40 to ensure that the profit is greater than $8,200.
Some applications involve computing interest earned on an investment during a specified time period. The interest can be computed as simple interest or compound interest.
Simple interest is based only on the initial deposit, which serves as the amount on which interest is computed, called the principal, for the entire time period. If the amount P is invested at a simple annual interest rate of r percent, then the value V of the investment at the end of t years is given by the formula
V = P(1+)
where P and V are in dollars.
In the case of compound interest, interest is added to the principal at regular time intervals, such as annually, quarterly, and monthly. Each time interest is added to the principal, the interest is said to be compounded. After each compounding, interest is earned on the new principal, which is the sum of the preceding principal and the interest just added. If the amount P is invested at an annual interest rate of r percent, compounded annually, then the value V of the investment at the end of t years is given by the formula
V =
If the amount P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formula
V =
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