Word Problems
1. To achieve the maximum benet for the heart when exercising. the heart rate {in beats per minute) shouid be in the target heart rate zone. The lower limit of this zone is found by taking 70% of the difference between 220 and the age of the person. The upper limit is found by using 55% of the difference. Complete parts a through d. a. Find formulas for the upper and lower limits (U and L) as linear equations involving the age it. b. What is the target heart rate zone for a 40-year-old? c. What is the target heart rate zone for a 60-year-old? d. Two women in an aerobics class stop to take their pulse and nd that they have the same pulse. One woman is 32 years older than the other and is working at the upper limit of her target heart rate zone. The younger woman is working at the lower limit of her target heart rate zone. What are the ages of the two women. and what is their pulse? Let x represent the age of the younger woman. So. the age of the older woman is X+32 YEARS. 2. The sales of a small company were 544.000 in its fourth year of operation and $54,000 in its fth year. Let y represent sales in the xth year of operation. Assume that the data can be approximated by a straight line. la) Find the slope of the sales line. and give an equation for the line in the form y=mx+b. (In) Use your answer from part (b) to nd out how many years must pass before the sales surpass $110,000. 3. Find an equation in slepe-intercept form for the line. Through (4,1) and (1.3) 4. A person is the manager of a rm. He is considering manufacturing a new product, so he asks the accounting department for cost estimates and the sales department for sales estimates. After he recer the data. he must decide whether to go ahead with production of the new product. Analyze the following data (nd a break-even quantity) and then decide what the manager would do in this case. Also. write the prot function. C(x)=160x+1200 and R(x)=140x 5. A rm produces a product that has the production cost function Clx)=435x+14.355 and the revenue function R[X)=530x. No more than 192 units can he sold. Find and analyze the breakeven quantity, then nd the prot function. E. To produce x units of a religious medal costs C(x)=13x+60. The revenue is R'X)=25)L Both cost and revenue are in dollars. 3. Find the break-even quantity. h. Find the prot from 530 units. 6. Find the number of units that must be produced for a protcf $ 120. i". The manager of a restaurant found that the cost to produce 100 cups of coffee is $1013, while the cost to produce 600 cups is $57.73. Assume the cost 60:) is a linear function of x, the number of cups produced. Answer parts a through f. a) Find a formula for C(x) b) What is the xed cost? c) Find the total cost of produdng 1000 cups. d) Find the total costof producing 1001 cups. 6) Find the marginal cost of the 1001 st cup f) What is the marginal cost of any cup and what does this mean to the manager? 3. Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one Tshirt is $3.50. Her total cost to produce 50 Tshirts is $255. and she sells them for $8 each, 3. Find the linear cost function for Joanna's T-shirt production. It. How many T-shirts must she produce and sell in orderto break even? 2:. How many T-shirts must she produce and sell to make a prot of $300
