In: Economics
A firm is deciding how to divide up its plastic between cellphones and toys. The production functions are:
Cellphones: C = 20PC – 1.5PC2
Toys: T = 80PT – 2PT2
Constraint: PC + PT = 60
Profit is $10 per cellphone and $5 per toy. How many units of plastic should be used for toys (PT)?
Enter as a value.
Solution:
Profit function of the firm:
And the constraint we got:
Therefore we have to maximize the profit function with respect to the constraint.
Taking Lagrange equation,
Now eq (i) and (ii) imples,
Eq(iii) implies,
Therefore, 40units of plastic should be used for toys.