Question

A company produces cars at three different plants in amounts x, y and z, respectively,
producing an annual revenue of f(x, y, z) = x
2
yz − 2(x + y + z). The company is to
produce 100 units annually. How should the production be distributed to maximize
the revenue? Solve this problem by using the Lagrange multiplier method.

Answer 1

Answer:

(a) The unit sale prices of x,y and z are respectivelyRs.2.50,Rs.1.50 and Rs.1.00.

Total revenue in market I can be represented as:

[10000200018000]⎣⎢⎢⎡2.501.501.00⎦⎥⎥⎤

=10000×2.50+2000×1.50+18000×1.00

=25000+3000+18000

=46000

Total revenue in market II can be represented as:

[6000200008000]⎣⎢⎢⎡2.501.501.00⎦⎥⎥⎤

=6000×2.50+20000×1.50+8000×1.00

=15000+30000+8000

=53000

So, the total revenue in market I is Rs 46000 and in market II is Rs.53000.

(b) The unit cost prices of x,y and z are respectively given as Rs.2.00, Rs.