Exercise 1.8
- Your long distance phone service has a base monthly charge anda per-minute charge. When you used 350 minutes in a month the totalcost was $32.50. When you used 400 minutes in a month the totalcost was $36.50. You want an equation that will allow you tocalculate your phone bill.
Please provide:
a. the definition of x, including the units
b. the definition of y, including the units
c. the equation in the form y = mx + b
d. the units of the slope
e. the units of b and an interpretation of b.
f. How much will your phone bill be if you talked for 711minutes?
2. The dosage for a medicine is linear with the weight of thepatient. There is a minimum dosage onto which is added a per pounddosage. You find that your dosage, at 110 pounds is 48 milliliters(ml). Your brother’s dosage, at 170 pounds, is 66 ml. You wouldlike an equation that will relate the dosage to the weight of thepatient. Please provide:
a. the definition of x, including the units
b. the definition of y, including the units
c. the equation in the form y = mx + b
d. the units of the slope
e. the units of b and an interpretation of b.
f. what is the dosage for a 165 lb patient?
For each of the problems,6 –10, cost information at a certainlevel of production for a manufacturing process is given. Therevenue per unit is also given. Assume a linear relationshipbetween the number of units produced and cost. For each problemplease find:a. The cost,revenue and profit functions and the unitsof the slope and of b.b. The variable cost per unit, also known asthe marginal cost, and the fixed cost. c. The cost, revenue andprofit when z units are produced. (z will be specified in eachproblem)d. The break-even point.e. The average cost per unit ofproducing w units and the equation of the average cost per unitfunction. (w will be specified in each problem)
- The cost of producing 1,250 units is $45,000. The cost ofproducing 1,500 units is $50,000. Each unit produced can be soldfor $30. z = 3,000; w = 2,500.
- The cost of producing 23,000 units is $225,000. The cost ofproducing 30,000 units is $260,000. Each unit produced can be soldfor $12. z = 45,000; w = 68,000.
