A company is planning to spend up to $10,000 on advertising. It costs $3,000 per minute to advertise on television and $1,000 per minute to advertise on radio.

If the company buys x minutes of television advertising and y minutes of radio advertising, its revenue in thousands of dollars is given by:

f (x, y) = - 2x^2 - y^2 + xy + 8x + 3y

Find the values of x and y that maximize the firms revenue while staying within its advertising budget.

Question

Business

Rachael Norton

2 July, 16:29

A company is planning to spend up to $10,000 on advertising. It costs $3,000 per minute to advertise on television and $1,000 per minute to advertise on radio.

If the company buys x minutes of television advertising and y minutes of radio advertising, its revenue in thousands of dollars is given by:

f (x, y) = - 2x^2 - y^2 + xy + 8x + 3y

Find the values of x and y that maximize the firms revenue while staying within its advertising budget.

+2

Answers (1)

Know the Answer?

Ellen Mercer · Answer 1

The company should hire 2 min in television and 3 min in radio.

Explanation:

This is a maximization problem. The first thing to do is to set the main equation given and to define the constrainsts. In this case the constraints are: 3x+1y ≤ 10, x ≥ 0, y ≥ 0 x and y are integers (since you only can hired entire minutes). An interation process with possible x, y combinations is the proper approach. If you do not use solver (Excel microsoft), you have to prove every x, y possible combination and visually identify the max outcome for revenues