Problem: The price demand equation and the total cost function for the weekly production of Toyota Cars, are given by
X = 100 — P and C(X) = x^3/100 + 30X
Where X stands for the quantity of cars produced and P for the unit price.
Part I: The aim of this part is to use the course technical skills in optimization to determine the optimal quantity produced, the optimal price and the maximum profit. Please show all calculations you have done with steps labeling each calculation like the critical values
Part II: Using the graphing strategy, show the graph of the profit function showing the maximum profit. All graphs will have x as the horizontal. The graph must be supported by the graphing strategy calculations you have done, this includes, the classification of all turning points, the intercepts and the domain of the problem.
Instruction: You must submit a full solution of the problem properly typed (or clearly handwritten) and a total of two graphs with proper labels and relevant information must be tagged properly like the breakeven point and any maxima/minima. I