Applied Mathematics for Business and Economics

Lecture Note Function of Two Variables

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3 A paint store carries two brands of latex paint. Sales figures indicate that if the
first brand is sold for x 1 dollars per gallon and the second for x 2 dollars per gallon,
the demand for the first brand will be Dxx 112 ( , )=−200 10x 1 + 20 x 2 gallons per
month and the demand for the second brand will be Dx 21 ( ,x 2 )=+− 100 5 x 110 x 2
gallons per month.
a. Express the paint store’s total monthly revenue from the sale of the paint
as a function of the prices x 1 andx 2.
b. Compute the revenue in part a. if the first brand is sold for $6 per gallon
and the second for $5 per gallon.
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Dxx 112 (), =−+200 10x 120 x 2

Dx 21 ( ,x 2 )=+−100 5x 110 x 2

1

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4 The output at a certain factory is QKL( , )= 120 K L23 13units, where K is the

capital investment measured in units of $1,000 and L the size of the labor force

measured in worker-hours.

a. Compute the output if the capital investment is $125,000 and the size of

the labor force is 1,331 worker-hours.

b. What will happen to the output in part a. if both the level of capital

investment and the size of the labor force are cut in half?

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1

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5 At a certain factory, the daily output is QKL( ,60)= K L12 13units, where K

denotes the capital investment measured in unit of $1,000 and L size of labor force

measured in worker-hours. Suppose that the current capital investment is

$900,000 and that 1,000 worker-hours of labor are used each day. Use marginal

1

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