QUESTION III Pierre-Hadrien is a pastry chef in the Parisian restaurant L'Ezcuse that serves crois- sants and palmiers for breakfast. Pierre-Hadrien needs to work under the daily prod- ucts' constraints imposed by the restaurant's owner. He sets up a linear optimization problem to maximize the restaurant's revenue from the sales of croissants and palmiers. Palmiers are sold for $4 each and croissants for $5 each. (Yes, ok, these should be €, but let's pretend a French cafe would accept $ for the sake of this exercise.) We assume that Pierre-Hadrien can sell all the palmiers and croissants he produces. Croissants and palmiers' production require varions quantities of butter, sugar, flour and eggs as specified in the table below. Palmiers Croissant Total Supplies per Day 200 Butter (g) 100 15000 300 Sugar (R) Flour (R) Eggs (units) 25000 17000 35 200 100 200 0.4 0.6* *Note that eggs are in decimals because pastry chefs typically bake the paste for maltiple pastries at once. A paste with 3 eggs can then produce 5 croissants. Your objective is to help Pierre-Hadrien maximizing his revenue using a linear optimization model. (a) Specify the decision variables, the objective function and the constraints for the model. You may aine that fractional values for the mumber of palmiers and croissants are acceptable. (b) Is the decision to make 30 palmiers and 50 croissants per day feasible? Why or why not? (c) Pierre-Hadrien wants to be loyal to the customers who prefer croissants. Specify one cotraint that can be added to the model that will ensure that at lesst 14 croissants are produced ench day. (d) Is the claim the objective value must increase as a result of ndding the constraint inn (c)" correct?