Question 4. (a) The total fixed costs, FC, for a company follows the normal distribution: FC-N(1200, 100%) The variable costs per unit produced, v, follows the probability distribution: v 2 3 4 5 Pr 0.1 0.4 0.4 0.1 The selling price per unit, p, follows the probability distribution: 6 7 8 9 Pr 0.1 0.4 0.4 0.1 The random numbers 0.7673, 0.2493, and 0.5660 are used to simulate FC, V, and p, respectively. Determine the simulated break-even quantity for this company. [& marks] (b) Bowls-R-Us Company manufactures two types of bowling balls: Heavy and Light. The profit margin on a heavy ball is 30 and the profit margin on a light ball is 25. It takes 1 pound or iron ore to make a heavy ball and 0.75 pounds of iron ore to make a light ball. The cost of iron ore is $20 per pound, and the company has no more than 10 pounds of iron are available. The company faces limited staffing which restricts total output to 19 balls. The company has pre-order for 6 heavy and 4 light balls that must be completed. (i) Calculate the maximum profit possible for Bowls-R-Us Company. [10 marks) (ii) If Bowls-R-Us produces only the number of balls that are pre-ordered, determine the slack in iron ore. [2 marks]