12) A statistical analysis program gives the function S =-48.914- -0.16AB+0.22B + 226.814+194.898 -712.71 as a two-variable, quadratic model for the average sales of Product A given the prices of Product A and Product B. [a] Use this model to estimate the average sales of Product A when the price of Product A is $2.90 and the price of Product B is $3.90. [b] Use this model to estimate the average sales of Product A when the price of Product A is $3.55 and the price of Product B is $3.15. [c] Use the model to find as aB [d] Use this model to calculate as DA \\( A,B)=(3.55,3.15) . Interpret the result.[e] Suppose the price of Product A increases from $3.55 to $3.57. Find the compensating change in the price of Product B that keeps the average sales equal to S(3.55, 3.15). [f] Is S(A.B) a reliable model for the average sales of Product A given the prices of Product A and Product B? Why or why not