Consider the supply contract problem scenario that we discussed in class (and in Chapter 4). That is, the seller (supplier) is MTO; the seller pays a fixed cost of $100, 000 to produce, and its per unit production cost is $35; the buyer pays the seller $80 per item purchased, and sells the items, for which there is a demand, for $125; the residual price is $20. The demand probability mass function was given in class. As discussed, the globally optimal solution which maximizes the combined expected profit, is for the buyer to purchase Q = 16, 000 items. This results in a combined expected profit of $1, 014, 500. Suppose that the buyer and seller do not share any information beyond that in the following contract: Suppose that the buyer and seller have a revenue sharing contract with C new B being the new cost per unit for the buyer in exchange for x% revenue sharing. Suppose C new B = CM = 35. Does there exist a value of x that will both: yield both the maximum combined expected profit and equally split it between the buyer and the seller? If so, determine this value of x. If not, explain why no such value exists.