Applied Mathematics for Business and Economics

Lecture Note Function of Two Variables

Qxy(),10= xy^2

Exercises

1 Using x skilled workers and y unskilled workers, a manufacturer can produce

units per day. Currently there are 20 skilled workers and 40

unskilled workers on the job.

a. How many units are currently being produced each day?

b. By how much will the daily production level change if 1 more skilled

worker is added to the current work force?

c. By how much will the daily production level change if 1 more unskilled

worker is added to the current work force?

d. By how much will the daily production level change if 1 more skilled

worker and 1 more unskilled worker are added to the current work force?

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Qxy(),10= xy^2

(Answer: a. 160,000 units per day, b. 16,400 units per day, c. 4000 units per day

d. 20,810 units per day)

2 A manufacturer can produce electric typewriters at a cost of $80 apiece and
manual typewriters at a cost of $20 apiece.
a. Express the manufacturer’s total monthly production cost as a function of
the number of electric typewriters and the number of manual typewriters
produced.
b. Compute the total monthly cost if 500 electric and 800 manual typewriters
are produced.
c. The manufacturer wants to increase the output of electric typewriters by 50
a month from the level in part b. What corresponding change should be
made in the monthly output of manual typewriters so that the total monthly
cost will not change?
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