Question

In: Economics

A firm is deciding how to divide up its plastic betweencellphones and toys. The production...

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.

Solutions

Expert Solution

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.

Rahul Sunny answered 2 years ago

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