Hello, I only need help answering 1c and 1d. i already answered 1a and 1b. If you want to see my code for 1a and 1b, comment back and I'll paste my code.

A companyI produces interior and exterior paint: from three rawI materials, M1, M2, and M3. The maximum daily available amounts of M1, M2, and M3 are 26, 12, and 15 tons, respectively. Table 1 shows the quantities of raw materials M1, M2, and M3 needed per ton of each exterior and interior paints. Toel Tons of raw material per ton of Exterior paint Interior paint Raw material, M1 5 6 Raw material, M2 Raw material, M3 The maximum daily demand for interior paint is 30tons, so the company should produce at most 30 tons of the interior paint per day. Profit per ton of interior paint is $70,000. Prot per ton ofthe exterior paint depends on its amount. Table 2 shows prot per ton of the exterior paint at different amounts. Tobie 2 Exterior - aint moon For example, if the production amount for the exterior paint is 7 tons. the prot from the exterior paint is calculated as follows: Prot = 60,000\" + 80,000'3 = 480,000 [Hint: The above prot ls equivalent to: 60,000'mini4,7} + 80,000'max17-4,0}] The companv wants to determine the optimal production quantities [In tons} of Interior and exterior paints such that the total daily prot is maximized. o) [5 points] Please dene the decision variables, the objective function, and constraints. Then, write the mathematical formulation of your optimization model. Please note that m should use mathematics! notation more: R mining m. b} [a points] Create a function in R that returns the objective value for feasible solutions and penalizes the infeasible solutions. it) [3 points] Use optimi} to solve your model. Save the optim's solution and its objective value in two variables with the names of your choice. :1} [4 points] Try 3 different methods to improve the optim's solution and discuss the results