Hello. I am looking for help with my homework. For numbers 1 and 3, I am looking to see if I did the problem correctly. For number 2, I am completely lost and don't know where to begin.

S(Subscript 1)= 30+20x-0.4x^2+b(subscript 1)y
S(Subscript n)=24.58+325.18(1-e^(-x/14))+b(subscript 1)y

1. What is ∂S(subscript 1)/∂x? Does this indicate that sales might actually decline after some amount is spent on TV advertising? If so, what is this amount?

20-.8x
Yes, 25 million.

2.Does the quadratic model S(subscript 1)(x,y) indicate that sales will become negative after some amount is spent in TV advertising?Does this model cease to be useful in prediciting sales after a certain point?

3. What is ∂Sn/ ∂x? Does this indicate that sales will continue to rise if additional money is devoted to TV advertising?

23.2271e^(-x/14)
No, it does not indicate that sales will continue to rise if add'l money is devoted to TV advertising

I'm assuming y and b_1 are being kept constant.

I don't find anything wrong with 1 or 3.

For 2;
Yes, if you drew the graph of the quadratic, you'll see that it's an inverted parabola. It starts at 30 + b_1y, rises to a maximum at 25 million and then falls down. Eventually, there will be a point where the sales will be = 0, then become negative.

To obtain that point, just solve the quadratic for S = 0. You'll get two answers, one of which is positive, the other negative. Since investment in advertising cannot be negative the point where the sales theoretically become negative is the other positive solution.

Thanks soooooo much! You're a big help!