4: [12 marks] Lingnan Bakery (LB) also makes and sells sponge cakes. Every day LB makes sponge cakes only once in the morning and LB will not consider another preparation on the same day. The sponge cakes cost $15 each to make, and LB sells each sponge cake for $35. Every day, 2 hours before the bakery closes, those unsold sponge cakes are reduced to $10 each and typically 75% of those leftovers are sold. Any unsold sponge cakes on the day will be discarded. Any demand cannot be met, LB will incur a loss of customer goodwill which is quantified as $2 each. The daily demand of sponge cakes can be approximated by a normal distribution with = 100 cakes and = 20 cakes. a. What inventory model should be used to determine the quantity of sponge cakes prepared daily to maximize the total expected daily profit? Why? [3 marks] b. What is the critical ratio (optimal service level)? [5 marks] c. Howmanyspongecakesshouldbemadedailytomaximizethetotaldailyexpectedprofitofthisproduct