pleas solve it carefully with clear steps for each one

2 .LP Formulation and graphical solution. (50 pts) A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food II' contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs 50$ per kg to purchase Food 'l' and 70$ per kg to purchase Food 'II'. Formulate this problem as a linear programming problem to minimize the cost of such a mixture. a. (5 pts) Define the decision variables. b. (5 pts) Write down the LP objective function. c. (10 pts) Write down the LP constraints. d. (10 pts) Graph the constraints. e. (5 pts) Shade the feasible region (5 pts) f. (10 pts) Determine the coordinates of the vertices of the feasible region. g. (5 pts) Identify and label the optimal solution in the figure. Give the optimal value of the objective function