4) (35) The profit function for selling widgets can be modeled by a quadratic equation of the form P(x) = ax2 + bx + c where x represents the price per widget. Consider the table of profits for various prices of widgets: Price(x) $ 3 5 10 Profit P(x) $ 47500 67500 30000 a) give a system of three equations and three unknowns to solve for the values of a, b, and C. Hint the price is x so substitute that in for x on the right hand side. The P(x) is on the right hand side. Youi will get three equations from this table. b) Rewrite the system of equations in matrix form. c) Find the inverse of matrix A by augmenting with the identity matrix and then performing Gauss Jordan Elimination. check your final answer with technology. d) give the profit function. Multiply [A-][C] to find a, b, and c. Show your work! e) Consider the new profit chart Price(x) $ 3 10 Profit P(x) $ 43000 95000 120000 f) Find the profit function by multiplying [A-!][C] to find a, b, and c. Note: the only thing changing is the constant matrix so you can use the same inverse matrix. Show your work