Please provide a clear explanation and solution, without using Excel.

Tango's Kiosk needs to decide how many pretzels to order for Spring Carnival. The pretzels cost $0.10 and sell for $0.25; unsold pretzels can be returned to the supplier for a $0.05 refund (the supplier then sells them in its Day Old Shopper for $0.15). Demand is estimated to be normal with mean 500 and standard deviation 100. a. How many pretzels should they order? b. Suppose the standard deviation of demand is 200. How many pretzels should be ordered now? What can you say about the relationship between order quantity and demand uncertainty (standard deviation)? c. Due to a surge in pretzel demand, the cost per pretzel to Tango's Kiosk goes up to $0.18; however, due to the extreme price-elasticity of CMU students, they can still only sell them for $0.25. Unsold pretzels still only fetch $0.05 upon return. Determine how many pretzels Tango's Kiosk should order when the standard deviation of demand is 100 and when the standard deviation of demand is 200. What do you note about the relationship between order quantity and demand uncertainty? Discuss why the relationship differs from (b). d. Suppose Tango's Kiosk decides to set the probability of a stock-out at 10% (i.e., the probability that total demand exceeds the order quantity is 10%). How many pretzels should be ordered if the standard deviation of demand is 200? AREAS OF THE CUMULATIVE STANDARD NORMAL DISTRIBUTION 0.92647 0.14686 0.00016 -0.90 10854 0.99781 0.72525 An entry in the table is the proportion under the curve cumulated from the negative tail. 2 Giz) GOZ) G2) -4.00 0.00003 -130 0.09680 140 0.91924 -3.95 0.00004 -125 0.10565 145 -3.90 0.00005 -120 0.11507 150 0.93319 -3.85 0.00006 -LIS 0.12507 155 30 -3.80 093943 0.00007 LIO 0.13567 160 094520 17 0.00009 -105 1 20 165 0.95053 -3.70 0.0001 -100 015866 12 0.95543 365 10 0.00013 LO -0.95 01706 15 0.95994 -3.60 0.18406 18 180 0.96407 -3.55 0.00019 -0.85 0.19766 18 185 0.96784 ---3.50 0.00023 -0.80 0.21186 1.90 0.97128 --3.45 0.00028 -0.75 0.22663 195 0.97441 -3.40 0.00034 -0.70 024196 2.00 0.97725 -3.35 0.00040 -0.65 0.25785 205 0.97982 -330 0.00048 -0.60 0.27425 210 0.98214 -3.25 0.00058 -0.55 0.29116 2.15 0.98422 -3.20 0.00069 -0.50 2.20 0.98610 0.00082 -0.45 52 032636 2.25 0.00097 0.98778 -3.0 0.31458 2.30 0.98928 -305 0.00114 -0.35 036317 -300 235 0.99061 0.00135 05 -2.95 0.00159 0.99180 -0.25 040170 200 0.40129 245 000182 0.99286 0.00187 -0.20 - 95 0.99379 0.00219 -289 00219 015 0.44038 OS 280 255 0.00256 0.44038 0.99461 -280 010 2,60 0.995 -225 0.00298 -0.0 048006 265 220 0.00347 0.99598 21 2.70 0.99653 265 0.00402 005 2. 0.51994 2.75 099702 -260 0.00466 010 053983 2.80 099244 -2.55 0.00539 Ols 0.55962 285 -2.50 0.00621 0.20 0.57926 2.90 0.99813 -245 0.00714 0.25 0.5987 2.95 0.99841 -2.40 0.00820 030 0.61791 3.00 0.99865 - 235 0.00939 0.35 0.63683 3.05 0.99886 -2.30 0.01072 0.40 0.65542 3.10 0.99903 - 2.25 0.01222 0.45 0.67364 3.5 0.99918 - 2.20 0.01390 0.50 0.69146 120 0.99931 -215 0.01578 0.55 0.70884 25 - 210 0.99942 20 0.01786 0.60 0.00 330 -205 0.02018 099952 065 0.7215 3335 WAS 099960 - 200 200 0.02225 0.70 0.75804 3:40 099966 -195 0.02559 0.75 077332 3:45 0.99972 -190 0.02872 0.80 0.78814 3.50 -185 0.03216 099977 0.85 0.80234 355 0.99981 -180 0.03593 0.90 0.81594 3.60 0.99984 -175 0.04006 0.95 0.82894 3.65 -170 0.99987 0.01457 100 0.84134 3.70 0.99989 --165 0.04947 LOS 0.85314 3.75 0.99991 -160 0.05480 10 0.86433 3.80 0.99993 -155 0.06057 U15 0.87493 3.85 0.99994 - 150 0.06681 120 0.88493 3.90 0.99995 -145 0.07353 5 0.89435 3.95 0.99996 -140 0.08076 130 0.90320 4.00 0.99997 -135 0.08851 135 0.91149 -0.40 0.30 2.40 250 0.38209 042074 0.46017 050000 000