Hello, Bobby!

We have the function: .4. An advertising agency spends dollars on a newspaper campaign

and a further dollars promoting client's products on local radio.

It receives a 15% commission on all sales that the client receives.

The agency has $10,000 to spend in total.

The client earns dollars from its sales

where: .

Use the method of Lagrange multipliers to determine how much should be spent

on advertising in newspapers and on radio to maximize the agency's net income.

Give your answers correct to two decimal places.

and the constraint: .

Our function is: .

Set the three partial derivatives equal to zero.

. .

. .

. .

From and , we have: .

. . Then: .

Substitute into : .

. .

Therefore: .

Note: the agency's income is

And someone check my work . . .please!

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