Problem 4: (25 points) The annual total inventory cost of the economic production quantity model is given by TC(Q)=QSD+2H(1PD)Q where Q is the production quantity per cycle, S is the setup cost, H is the holding cost per unit per year, D is the annual demand rate, and P is the annual production rate. 4- Show that the economic production quantity is given by Q=r(1pD)25 b. Show that the minimum annual total cost is given by TC(Q)=2SDH(1FD) c- A product is demanded at a monthly rate of 450 units. It costs AED 24 to store one unit. of the product for one year. It costs AED 120 to setup the production facility in order to manufacture the product. The actual annual production rate is 7200 units per year. Find the economic production quantity, the minimum total inventory costs, and the minimum number of setups per year. d. Due to some constraint's, the facility can only produce 400 units of the product after each setup. What is the effects of this restriction on the total inventory cost