We are given that revenue of Tacos is given by the mathematical expression .
(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.
(B) Let us factor the given revenue expression.
Therefore, correct option for part (B) is the third option.
(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.
(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.
(E) The table is attached.
Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.
