In this problem, the model is already built.$$ Don't change the formulas in the gray section.$$ The model below describes an inventory decision.$$ There are $10$ potential customers, each has the same probability of buying the product. The product is perishable, so if the owner orders more than are sold, she loses $$180$ per unsold item.$$ If she orders too few, then she has an opportunity loss, of $$100$ per unit that she could have made if she ordered more.$$ There are $11$ possible demands that could occur, $0$ through $10$ units demanded.$$ The model computes the probability of each of those states from the individual prob. of buying $($in C$13)$ using a binomial distribution.$$ The cost column computes the cost for that demand, given the amount ordered.$$ Total cost is sum of probability times cost.$$ Input parameters $$ Demand Probability Cost $$ Cost of having extra $$18000\mathrm{.}000900\mathrm{.}0$ Cost of running out $$10010\mathrm{.}000720\mathrm{.}020\mathrm{.}000540\mathrm{.}0$ Amount ordered $530\mathrm{.}000360\mathrm{.}040\mathrm{.}000180\mathrm{.}050\mathrm{.}0000\mathrm{.}0$ Individual probability of buying $160\mathrm{.}000100\mathrm{.}070\mathrm{.}000200\mathrm{.}080\mathrm{.}000300\mathrm{.}090\mathrm{.}000400\mathrm{.}0101\mathrm{.}000500\mathrm{.}0$ Total Cost $500\mathrm{.}0$

Using references to cells in the model, make a two way data table with individual probability of buying going from $0$ to $1$ by $\mathrm{.}1$ on the row and amount ordered going from $1$ to $10$ on the column.$$ The table will be showing total cost. Looking at the table, answer the following questions. a$.$ If the individual probability of buying is $0\mathrm{.}3,$ what is the best quantity to order? $5$ b$.$ If the individual probability of buying is $0\mathrm{.}7,$ what is the best quantity to order? $9$ c$.$ Suppose the company found a way to sell unused product for a discount price so that the cost of having extra dropped from $180$ to $50.$ Now what is the$$ best quantity to order for $0\mathrm{.}3$ prob of buying? $$ d$.$ For $0\mathrm{.}7$ probability of buying?