Question: Appendix: Standard Normal Loss Function Table Appendix: Standard Normal Distribution Table ( Z table) The All-Colorful Company produces a variety of paint products. Demand is

( Z table) The All-Colorful Company produces a variety of paint products.

Demand is highly seasonal, and the forecasted demand (in gallons) for the

next 4 quarters is given as follows: The All-Colorful Company has a

Appendix: Standard Normal Loss Function Table Appendix: Standard Normal Distribution Table ( Z table) The All-Colorful Company produces a variety of paint products. Demand is highly seasonal, and the forecasted demand (in gallons) for the next 4 quarters is given as follows: The All-Colorful Company has a regular-time production capacity of 90,000 working hours per quarter for Quarters 1,2, and 4, and the regular-time production capacity of Quarter 3 is 150,000 working hours. Besides regular-time production, the All-Colorful Company can also use overtime production or subcontracting. The maximum overtime working hours in any quarter is 20% of regular-time capacity. Each gallon requires 0.2 working hour of production. The subcontractor can supply a maximum of 200,000 gallons per quarter. The All-Colorful Company has an initial inventory of 250,000 gallons at the beginning of Quarter 1, and the ending inventory at the end of Quarter 4 should be 300,000 gallons. Regular-time cost is $10 per hour, overtime cost is $15 per hour, subcontracting cost is $4 per gallon, and the inventory holding cost is $3 per gallon per quarter. Assume no backorders or stockouts are permitted. Formulate a linear program to determine the best production plan. Appendix: Standard Normal Loss Function Table (continued) Standard Normal Loss Function Table, L(z) (Concluded) \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hlinez & 0.00 & 0.01 & 0.02 & 0.03 & 0.04 & 0.05 & 0.06 & 0.07 & 0.08 & 0.09 \\ \hline 0.0 & 0.3989 & 0.3940 & 0.3890 & 0.3841 & 0.3793 & 0.3744 & 0.3697 & 0.3649 & 0.3602 & 0.3556 \\ \hline 0.1 & 0.3509 & 0.3464 & 0.3418 & 0.3373 & 0.3328 & 0.3284 & 0.3240 & 0.3197 & 0.3154 & 0.3111 \\ \hline 0.2 & 0.3069 & 0.3027 & 0.2986 & 0.2944 & 0.2904 & 0.2863 & 0.2824 & 0.2784 & 0.2745 & 0.2706 \\ \hline 0.3 & 0.2668 & 0.2630 & 0.2592 & 0.2555 & 0.2518 & 0.2481 & 0.2445 & 0.2409 & 0.2374 & 0.2339 \\ \hline 0.4 & 0.2304 & 0.2270 & 0.2236 & 0.2203 & 0.2169 & 0.2137 & 0.2104 & 0.2072 & 0.2040 & 0.2009 \\ \hline 0.5 & 0.1978 & 0.1947 & 0.1917 & 0.1887 & 0.1857 & 0.1828 & 0.1799 & 0.1771 & 0.1742 & 0.1714 \\ \hline 0.6 & 0.1687 & 0.1659 & 0.1633 & 0.1606 & 0.1580 & 0.1554 & 0.1528 & 0.1503 & 0.1478 & 0.1453 \\ \hline 0.7 & 0.1429 & 0.1405 & 0.1381 & 0.1358 & 0.1334 & 0.1312 & 0.1289 & 0.1267 & 0.1245 & 0.1223 \\ \hline 0.8 & 0.1202 & 0.1181 & 0.1160 & 0.1140 & 0.1120 & 0.1100 & 0.1080 & 0.1061 & 0.1042 & 0.1023 \\ \hline 0.9 & 0.1004 & 0.0986 & 0.0968 & 0.0950 & 0.0933 & 0.0916 & 0.0899 & 0.0882 & 0.0865 & 0.0849 \\ \hline 1.0 & 0.0833 & 0.0817 & 0.0802 & 0.0787 & 0.0772 & 0.0757 & 0.0742 & 0.0728 & 0.0714 & 0.0700 \\ \hline 1.1 & 0.0686 & 0.0673 & 0.0659 & 0.0646 & 0.0634 & 0.0621 & 0.0609 & 0.0596 & 0.0584 & 0.0573 \\ \hline 1.2 & 0.0561 & 0.0550 & 0.0538 & 0.0527 & 0.0517 & 0.0506 & 0.0495 & 0.0485 & 0.0475 & 0.0465 \\ \hline 1.3 & 0.0455 & 0.0446 & 0.0436 & 0.0427 & 0.0418 & 0.0409 & 0.0400 & 0.0392 & 0.0383 & 0.0375 \\ \hline 1.4 & 0.0367 & 0.0359 & 0.0351 & 0.0343 & 0.0336 & 0.0328 & 0.0321 & 0.0314 & 0.0307 & 0.0300 \\ \hline 1.5 & 0.0293 & 0.0286 & 0.0280 & 0.0274 & 0.0267 & 0.0261 & 0.0255 & 0.0249 & 0.0244 & 0.0238 \\ \hline 1.6 & 0.0232 & 0.0227 & 0.0222 & 0.0216 & 0.0211 & 0.0206 & 0.0201 & 0.0197 & 0.0192 & 0.0187 \\ \hline 1.7 & 0.0183 & 0.0178 & 0.0174 & 0.0170 & 0.0166 & 0.0162 & 0.0158 & 0.0154 & 0.0150 & 0.0146 \\ \hline 1.8 & 0.0143 & 0.0139 & 0.0136 & 0.0132 & 0.0129 & 0.0126 & 0.0123 & 0.0119 & 0.0116 & 0.0113 \\ \hline 1.9 & 0.0111 & 0.0108 & 0.0105 & 0.0102 & 0.0100 & 0.0097 & 0.0094 & 0.0092 & 0.0090 & 0.0087 \\ \hline 2.0 & 0.0085 & 0.0083 & 0.0080 & 0.0078 & 0.0076 & 0.0074 & 0.0072 & 0.0070 & 0.0068 & 0.0066 \\ \hline 2.1 & 0.0065 & 0.0063 & 0.0061 & 0.0060 & 0.0058 & 0.0056 & 0.0055 & 0.0053 & 0.0052 & 0.0050 \\ \hline 2.2 & 0.0049 & 0.0047 & 0.0046 & 0.0045 & 0.0044 & 0.0042 & 0.0041 & 0.0040 & 0.0039 & 0.0038 \\ \hline 2.3 & 0.0037 & 0.0036 & 0.0035 & 0.0034 & 0.0033 & 0.0032 & 0.0031 & 0.0030 & 0.0029 & 0.0028 \\ \hline 2.4 & 0.0027 & 0.0026 & 0.0026 & 0.0025 & 0.0024 & 0.0023 & 0.0023 & 0.0022 & 0.0021 & 0.0021 \\ \hline 2.5 & 0.0020 & 0.0019 & 0.0019 & 0.0018 & 0.0018 & 0.0017 & 0.0017 & 0.0016 & 0.0016 & 0.0015 \\ \hline 2.6 & 0.0015 & 0.0014 & 0.0014 & 0.0013 & 0.0013 & 0.0012 & 0.0012 & 0.0012 & 0.0011 & 0.0011 \\ \hline 2.7 & 0.0011 & 0.0010 & 0.0010 & 0.0010 & 0.0009 & 0.0009 & 0.0009 & 0.0008 & 0.0008 & 0.0008 \\ \hline 2.8 & 0.0008 & 0.0007 & 0.0007 & 0.0007 & 0.0007 & 0.0006 & 0.0006 & 0.0006 & 0.0006 & 0.0006 \\ \hline 2.9 & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0005 & 0.0004 & 0.0004 & 0.0004 & 0.0004 \\ \hline 3.0 & 0.0004 & 0.0004 & 0.0004 & 0.0003 & 0.0003 & 0.0003 & 0.0003 & 0.0003 & 0.0003 & 0.0003 \\ \hline 3.1 & 0.0003 & 0.0003 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 \\ \hline 3.2 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0002 & 0.0001 & 0.0001 & 0.0001 & 0.0001 \\ \hline 3.3 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 \\ \hline 3.4 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0001 \\ \hline 3.5 & 0.0001 & 0.0001 & 0.0001 & 0.0001 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.6 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.7 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.8 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 3.9 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline 4.0 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \hline \end{tabular}

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