Acompany 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.

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

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this