Use Appendix 14A. EShack sells an ergonomic keyboard in one of its stores. Average weekly demand for this keyboard follows a Poisson distribution with mean 0.8 unit. It submits orders to the supplier weekly and the supplier delivers with a two-week lead time. a. Suppose it uses an order-up-to level of five. What is its average order quantity? Note: Round your answer to 1 decimal place. b. Suppose it uses an order-up-to level of nine. What is its expected on-hand inventory? Note: Round your answer to 1 decimal place. c. Suppose it uses an order-up-to level of six. What is its expected on-order inventory? Note: Round your answer to 1 decimal place. d. Suppose it uses an order-up-to level of seven. What is its in-stock probability? Note: Round your answer to 4 decimal places. e. Suppose it uses an order-up-to level of four. What is its stockout probability? Note: Round your answer to 4 decimal places. f. Suppose it wants a 0.97 in-stock probability. What should its order-up-to level be? \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{11}{|c|}{ Mean } \\ \hline \multicolumn{3}{|c|}{0.1} & \multicolumn{2}{|c|}{0.2} & \multicolumn{2}{|c|}{0.3} & \multicolumn{2}{|c|}{0.4} & \multicolumn{2}{|c|}{0.5} \\ \hlineS & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) \\ \hline 0 & 0.9048 & 0.00 & 0.8187 & 0.00 & 0.7408 & 0.00 & 0.6703 & 0.00 & 0.6065 & 0.00 \\ \hline 2 & 0.9998 & 1.90 & 0.9989 & 1.80 & 0.9964 & 1.70 & 0.9921 & 1.61 & 0.9856 & 1.52 \\ \hline 3 & 1.0000 & 2.90 & 0.9999 & 2.80 & 0.9997 & 2.70 & 0.9992 & 2.60 & 0.9982 & 2.50 \\ \hline 4 & 1.0000 & 3.90 & 1.0000 & 3.80 & 1.0000 & 3.70 & 0.9999 & 3.60 & 0.9998 & 3.50 \\ \hline 5 & 1.0000 & 4.90 & 1.0000 & 4.80 & 1.0000 & 4.70 & 1.0000 & 4.60 & 1.0000 & 4.50 \\ \hline \multicolumn{11}{|c|}{ Mean } \\ \hline \multicolumn{3}{|c|}{0.6} & \multicolumn{2}{|c|}{0.7} & \multicolumn{2}{|c|}{0.8} & \multicolumn{2}{|c|}{0.9} & \multicolumn{2}{|c|}{0.10} \\ \hlineS & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) \\ \hline 0 & 0.5488 & 0.00 & 0.4966 & 0.00 & 0.4493 & 0.00 & 0.4066 & 0.00 & 0.3679 & 0.00 \\ \hline 1 & 0.8781 & 0.55 & 0.8442 & 0.50 & 0.8088 & 0.45 & 0.7725 & 0.41 & 0.7358 & 0.37 \\ \hline 2 & 0.9769 & 1.43 & 0.9659 & 1.34 & 0.9526 & 1.26 & 0.9371 & 1.18 & 0.9197 & 1.10 \\ \hline 3 & 0.9966 & 2.40 & 0.9942 & 2.31 & 0.9909 & 2.21 & 0.9865 & 2.12 & 0.9810 & 2.02 \\ \hline 4 & 0.9996 & 3.40 & 0.9992 & 3.30 & 0.9986 & 3.20 & 0.9977 & 3.10 & 0.9963 & 3.00 \\ \hline 6 & 1.0000 & 5.40 & 1.0000 & 5.30 & 1.0000 & 5.20 & 1.0000 & 5.10 & 0.9999 & 5.00 \\ \hline 7 & 1.0000 & 6.40 & 1.0000 & 6.30 & 1.0000 & 6.20 & 1.0000 & 6.10 & 1.0000 & 6.00 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{11}{|c|}{ Mean } \\ \hline \multicolumn{3}{|c|}{1.2} & \multicolumn{2}{|c|}{1.4} & \multicolumn{2}{|c|}{1.6} & \multicolumn{2}{|c|}{1.8} & \multicolumn{2}{|c|}{2.0} \\ \hlineS & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) \\ \hline 0 & 0.3012 & 0.00 & 0.2466 & 0.00 & 0.2019 & 0.00 & 0.1653 & 0.00 & 0.1353 & 0.00 \\ \hline 1 & 0.6626 & 0.30 & 0.5918 & 0.25 & 0.5249 & 0.20 & 0.4628 & 0.17 & 0.4060 & 0.14 \\ \hline 2 & 0.8795 & 0.96 & 0.8335 & 0.84 & 0.7834 & 0.73 & 0.7306 & 0.63 & 0.6767 & 0.54 \\ \hline 3 & 0.9662 & 1.84 & 0.9463 & 1.67 & 0.9212 & 1.51 & 0.8913 & 1.36 & 0.8571 & 1.22 \\ \hline 4 & 0.9923 & 2.81 & 0.9857 & 2.62 & 0.9763 & 2.43 & 0.9636 & 2.25 & 0.9473 & 2.08 \\ \hline 5 & 0.9985 & 3.80 & 0.9968 & 3.60 & 0.9940 & 3.41 & 0.9896 & 3.21 & 0.9834 & 3.02 \\ \hline 6 & 0.9997 & 4.80 & 0.9994 & 4.60 & 0.9987 & 4.10 & 0.9974 & 4.20 & 0.9955 & 4.01 \\ \hline 7 & 1.0000 & 5.80 & 0.9999 & 5.60 & 0.9997 & 5.40 & 0.9994 & 5.20 & 0.9989 & 5.00 \\ \hline \multicolumn{11}{|c|}{ Mean } \\ \hline \multicolumn{3}{|c|}{2.2} & \multicolumn{2}{|c|}{2.4} & \multicolumn{2}{|c|}{2.6} & \multicolumn{2}{|c|}{2.8} & \multicolumn{2}{|c|}{3.0} \\ \hlineS & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) \\ \hline 0 & 0.1108 & 0.00 & 0.0907 & 0.00 & 0.0743 & 0.00 & 0.0608 & 0.00 & 0.0498 & 0.00 \\ \hline 1 & 0.3546 & 0.11 & 0.3084 & 0.09 & 0.2674 & 0.07 & 0.2311 & 0.06 & 0.1991 & 0.05 \\ \hline 2 & 0.6227 & 0.47 & 0.5697 & 0.40 & 0.5184 & 0.34 & 0.4695 & 0.29 & 0.4232 & 0.25 \\ \hline 3 & 0.8194 & 1.09 & 0.7787 & 0.97 & 0.7360 & 0.86 & 0.6919 & 0.76 & 0.6472 & 0.67 \\ \hline 4 & 0.9275 & 1.91 & 0.9041 & 1.75 & 0.8774 & 1.60 & 0.8477 & 1.45 & 0.8153 & 1.32 \\ \hline 5 & 0.9751 & 2.83 & 0.9643 & 2.65 & 0.9510 & 2.47 & 0.9349 & 2.30 & 0.9161 & 2.13 \\ \hline 6 & 0.9925 & 3.81 & 0.9884 & 3.62 & 0.9828 & 3.42 & 0.9756 & 3.24 & 0.9665 & 3.05 \\ \hline 7 & 0.9980 & 4.80 & 0.9967 & 4.60 & 0.9947 & 4.41 & 0.9919 & 4.21 & 0.9881 & 4.02 \\ \hline 8 & 0.9995 & 5.80 & 0.9991 & 5.60 & 0.9985 & 5.40 & 0.9976 & 5.20 & 0.9962 & 5.01 \\ \hline 9 & 0.9999 & 6.80 & 0.9998 & 6.60 & 0.9996 & 6.40 & 0.9993 & 6.20 & 0.9989 & 6.00 \\ \hline 10 & 1.0000 & 7.80 & 1.0000 & 7.60 & 0.9999 & 7.40 & 0.9998 & 7.20 & 0.9997 & 7.00 \\ \hline 11 & 1.0000 & 8.80 & 1.0000 & 8.60 & 1.0000 & 8.40 & 1.0000 & 8.20 & 0.9999 & 8.00 \\ \hline 12 & 1.0000 & 9.80 & 1.0000 & 9.60 & 1.0000 & 9.40 & 1.0000 & 9.20 & 1.0000 & 9.00 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{11}{|c|}{ Mean } \\ \hline \multicolumn{3}{|c|}{3.2} & \multicolumn{2}{|c|}{3.4} & \multicolumn{2}{|c|}{3.6} & \multicolumn{2}{|c|}{3.8} & \multicolumn{2}{|c|}{4.0} \\ \hlineS & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) & F(S) & I(S) \\ \hline 0 & 0.0408 & 0.00 & 0.0334 & 0.00 & 0.0273 & 0.00 & 0.0224 & 0.00 & 0.0183 & 0.00 \\ \hline 1 & 0.1712 & 0.04 & 0.4168 & 0.03 & 0.1257 & 0.03 & 0.1074 & 0.02 & 0.0916 & 0.02 \\ \hline 2 & 0.3799 & 0.21 & 0.3397 & 0.18 & 0.3027 & 0.15 & 0.2689 & 0.13 & 0.2381 & 0.11 \\ \hline 3 & 0.6025 & 0.59 & 0.5584 & 0.52 & 0.5152 & 0.46 & 0.4735 & 0.40 & 0.4335 & 0.35 \\ \hline 4 & 0.7806 & 1.19 & 0.7442 & 1.08 & 0.7064 & 0.97 & 0.6678 & 0.87 & 0.6288 & 0.78 \\ \hline 5 & 0.8946 & 1.97 & 0.8705 & 1.82 & 0.8441 & 1.68 & 0.8156 & 1.54 & 0.7851 & 1.41 \\ \hline 6 & 0.9554 & 2.87 & 0.9421 & 2.69 & 0.9267 & 2.52 & 0.9091 & 2.36 & 0.8893 & 2.20 \\ \hline 7 & 0.9832 & 3.82 & 0.9769 & 3.64 & 0.9692 & 3.45 & 0.9599 & 3.26 & 0.9489 & 3.08 \\ \hline 8 & 0.9943 & 4.81 & 0.9917 & 4.61 & 0.9883 & 4.42 & 0.9840 & 4.22 & 0.9786 & 403 \\ \hline 9 & 0.9982 & 5.80 & 0.9973 & 5.60 & 0.9960 & 5.41 & 0.9942 & 5.21 & 0.9919 & 5.01 \\ \hline 10 & 0.9995 & 6.80 & 0.9992 & 6.60 & 0.9987 & 6.40 & 0.9981 & 6.20 & 0.9972 & 6.00 \\ \hline 11 & 0.9999 & 7.80 & 0.9998 & 7.60 & 0.9996 & 7.40 & 0.9994 & 7.20 & 0.9991 & 7.00 \\ \hline 12 & 1.0000 & 8.80 & 0.9999 & 8.60 & 0.9999 & 8.40 & 0.9998 & 8.20 & 0.9997 & 8.00 \\ \hline 13 & 1.0000 & 9.80 & 1.0000 & 9.60 & 1.0000 & 9.40 & 1.0000 & 9.20 & 0.9999 & 9.00 \\ \hline \end{tabular}