Toyota faces the following demand curves for its Camry (C) and Avalon (A) lines

QC = 1500000 - 5PC^3+ .0002log(PA+1)      

 (where QC is quantity of C and PC is price of C and PA is price of A)

QA = 10000 - 7PA + .00015PC^4

Avalons are produced in two plants: X and Y. The amount of labor to produce an Avalon in plant X is 70 labor hours and in plant Y is 72 labor hours.

Camry’s are also produced in plants X and Y. The amount of labor to produce a Camry in plant X is 69 labor hours and in plant Y is 70 labor hours.

Labor is paid $25 an hour.

There are a total of 120,000 labor hours available for plant X,

There are a total of 90,000 labor hours available for plant Y.

Material costs per Camry are $200 while material costs per Avalon are $270.

WRITE TOYOTA’S OBJECTIVE AND CONSTRAINTS OUT AS A LINGO PROGRAM. BE CAREFUL. Make sure you get all the details.