A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $55 each to make and they sell for $64 each. The price of leftover wedding cakes is reduced by 50% on Mondays to clear out inventory. Demand for the weekend is normally distributed with a mean of 109 and a standard deviation of 13.

What is the optimal number of wedding cakes to stock on the weekend?

My real question is, how do I figure out if I will have a positive or negative z value given the problem and the z-table below? This is the z-table allowed on the exam.

\begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{\begin{tabular}{l} What is the optimal number of \\ wedding cakes to stock on the \\ weekend? \end{tabular}} \\ \hline \multicolumn{3}{|c|}{ Step 1: List out Variables } \\ \hline \multicolumn{2}{|c|}{ Demand } & 109 \\ \hline \multicolumn{2}{|c|}{ Standard Dev ()} & 13 \\ \hline \multicolumn{2}{|c|}{ Cost of Cake } & 55.00 \\ \hline \multicolumn{2}{|c|}{ Selling Price } & 64.00 \\ \hline \multicolumn{2}{|c|}{ Reduced Price 50%} & 32.00 \\ \hline \multicolumn{3}{|c|}{ Step 2: Find Cs \& Co } \\ \hline \multicolumn{2}{|c|}{ Cs = Selling-Cost } & 9 \\ \hline \multicolumn{2}{|c|}{ Co = Cost-Salvage } & 23 \\ \hline \multicolumn{2}{|c|}{Cs/(Cs+Co)} & 2813 \\ \hline \multicolumn{3}{|c|}{ Step 2: Find 2 -score and D+z } \\ \hline z-score & \multicolumn{2}{|c|}{-0.58} \\ \hlinez & \multicolumn{2}{|c|}{-7.5400} \\ \hlineD+z & \multicolumn{2}{|c|}{101.4600} \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{11}{|c|}{ Area from positive z-value to left tail } \\ \hline values & 0.00 & 0.01 & 0.02 & 0.03 & 0.04 & 0.05 & 0.06 & 0.07 & 0.08 & 0.09 \\ \hline 0.00 & 0.5000 & 0.5040 & 0.5080 & 0.5120 & 0.5160 & 0.5199 & 0.5239 & 0.5279 & 0.5319 & 0.5359 \\ \hline 0.10 & 0.5398 & 0.5438 & 0.5478 & & & 0.5596 & .5636 & 0.5675 & .5714 & 0.5753 \\ \hline 0.20 & 0.579 & 0.58 & & & & & a & & & \\ \hline 0.30 & y & & & & & & & & & \\ \hline 0.40 & 0.6554 & 0.6591 & 28 & 64 & 00 & 736 & 3772 & 6808 & 6844 & 6879 \\ \hline 0.50 & 0.6915 & 0.6950 & 6985 & 7019 & 7054 & 7088 & 7123 & .7157 & 7190 & 0.7224 \\ \hline 0.60 & 0.7257 & 0.7291 & .7324 & 1.7357 & 0.7389 & 0.7422 & .7454 & 0.7486 & 0.7517 & 0.7549 \\ \hline 0.70 & 0.7580 & 0.7611 & 0.7642 & 0.7673 & 0.7 & & & 0.7794 & & 0.7852 \\ \hline 0.80 & 0.7881 & 0.7910 & & & & & & & & \\ \hline 0.90 & 0.81 & 0 & & & & & & & & \\ \hline 1.00 & 0.84 & 0 & & & & & & & & \\ \hline 1.10 & 0.86 & 0 & 86 & & & & & & & \\ \hline 1.20 & 0.8849 & 9 & 88 & & 25 & 44 & 62 & & & 9015 \\ \hline 1.30 & 0.9032 & 9 & 66 & & 99 & 15 & 31 & 47 & 62 & 171 \\ \hline 1.40 & . & & & & & & & & & \\ \hline 1.50 & 0.93 & & & & & & & & & \\ \hline 1.60 & & & & & & & & & & \\ \hline 1.7 & 0 & & & & & & & & & \\ \hline 1.80 & 0 & 0 & 0.96 & & & & & & & \\ \hline 1.90 & 0. & 0 & 26 & & 8 & 44 & & & & 0.9767 \\ \hline 2.00 & 0.977 & 0 & 33 & ? & 3 & 98 & 03 & 08 & 12 & 0.9817 \\ \hline 2.10 & 0 & & & & & & & & & 857 \\ \hline 2.20 & 0.9861 & 0.9864 & 0.9868 & 1 & & & & & & 0.9890 \\ \hline 2.30 & 0.9893 & 0.9896 & & & & & & & & 0.9916 \\ \hline 2.40 & & & & & & & & & & \\ \hline 2.50 & & & & & & & & & & \\ \hline 20 & & & & & & & & & & \\ \hline & & & & & & & & & & \\ \hline & & & & & & & & & & \\ \hline & 0.9981 & & 0.9982 & & & 0.9984 & 0.9985 & 0.9985 & 0.9986 & 0.9986 \\ \hline 3.00 & 0.9987 & 0.9987 & 0.9987 & 0.9988 & 0.9988 & 0.9989 & 0.9989 & 0.9989 & 0.9990 & 0.9990 \\ \hline \end{tabular}