AEM 805_AA_HW1

Question 1 A:

REGULAR PLAN EXECUTIVE PLAN

$75.00 $150.00

$0.35 $0.30

3000 3000

1800 2200

1200 800

$420.00 $240.00

$495.00 $390.00

$105.00

QUESTION 1B

1800Volume of mins Regular 2200

0 75 Executive1 15023

1800 751801 75.35 1501802 75.7 1501803 76.05 1501804 76.4 1501805 76.75 1501806 77.1 150

Fixed Fee for 1800mins =

Fixed Fee for 2200mins =

Fee/mins after extra mins =

Fee/mins after extra mins =

Volume of mins used/month =

Volume of mins used/month =

Mins. Covered by fixed fee =

Mins. Covered by fixed fee =

remaining mins charged/mins =

remaining mins charged/mins =

Total variable fee/month =

Total variable fee/month =

Total Expenses per month =

Total Expenses per month =

Julie should chose the executive plan because she will safe a cost of $105 on expenses ( i.e: 495-390).

Juli need to be indiffernt at that volume of minutes where the expenses of the two plans are equal. Fixed fee + (variable fee*extra volume)= total expenses

1807 77.45 1501808 77.8 1501809 78.15 1501810 78.5 1501811 78.85 1501812 79.2 1501813 79.55 1501814 79.9 1501815 80.25 1501816 80.6 1501817 80.95 1501818 81.3 1501819 81.65 1501820 82 1501821 82.35 1501822 82.7 1501823 83.05 1501824 83.4 1501825 83.75 1501826 84.1 1501827 84.45 1501828 84.8 1501829 85.15 1501830 85.5 1501831 85.85 1501832 86.2 1501833 86.55 1501834 86.9 1501835 87.25 1501836 87.6 1501837 87.95 1501838 88.3 1501839 88.65 1501840 89 1501841 89.35 1501842 89.7 1501843 90.05 1501844 90.4 1501845 90.75 1501846 91.1 1501847 91.45 1501848 91.8 1501849 92.15 1501850 92.5 1501851 92.85 150

1852 93.2 1501853 93.55 1501854 93.9 1501855 94.25 1501856 94.6 1501857 94.95 1501858 95.3 1501859 95.65 1501860 96 1501861 96.35 1501862 96.7 1501863 97.05 1501864 97.4 1501865 97.75 1501866 98.1 1501867 98.45 1501868 98.8 1501869 99.15 1501870 99.5 1501871 99.85 1501872 100.2 1501873 100.55 1501874 100.9 1501875 101.25 1501876 101.6 1501877 101.95 1501878 102.3 1501879 102.65 1501880 103 1501881 103.35 1501882 103.7 1501883 104.05 1501884 104.4 1501885 104.75 1501886 105.1 1501887 105.45 1501888 105.8 1501889 106.15 1501890 106.5 1501891 106.85 1501892 107.2 1501893 107.55 1501894 107.9 1501895 108.25 1501896 108.6 150

1897 108.95 1501898 109.3 1501899 109.65 1501900 110 1501901 110.35 1501902 110.7 1501903 111.05 1501904 111.4 1501905 111.75 1501906 112.1 1501907 112.45 1501908 112.8 1501909 113.15 1501910 113.5 1501911 113.85 1501912 114.2 1501913 114.55 1501914 114.9 1501915 115.25 1501916 115.6 1501917 115.95 1501918 116.3 1501919 116.65 1501920 117 1501921 117.35 1501922 117.7 1501923 118.05 1501924 118.4 1501925 118.75 1501926 119.1 1501927 119.45 1501928 119.8 1501929 120.15 1501930 120.5 1501931 120.85 1501932 121.2 1501933 121.55 1501934 121.9 1501935 122.25 1501936 122.6 1501937 122.95 1501938 123.3 1501939 123.65 1501940 124 1501941 124.35 150

1942 124.7 1501943 125.05 1501944 125.4 1501945 125.75 1501946 126.1 1501947 126.45 1501948 126.8 1501949 127.15 1501950 127.5 1501951 127.85 1501952 128.2 1501953 128.55 1501954 128.9 1501955 129.25 1501956 129.6 1501957 129.95 1501958 130.3 1501959 130.65 1501960 131 1501961 131.35 1501962 131.7 1501963 132.05 1501964 132.4 1501965 132.75 1501966 133.1 1501967 133.45 1501968 133.8 1501969 134.15 1501970 134.5 1501971 134.85 1501972 135.2 1501973 135.55 1501974 135.9 1501975 136.25 1501976 136.6 1501977 136.95 1501978 137.3 1501979 137.65 1501980 138 1501981 138.35 1501982 138.7 1501983 139.05 1501984 139.4 1501985 139.75 1501986 140.1 150

1987 140.45 1501988 140.8 1501989 141.15 1501990 141.5 1501991 141.85 1501992 142.2 1501993 142.55 1501994 142.9 1501995 143.25 1501996 143.6 1501997 143.95 1501998 144.3 1501999 144.65 1502000 145 1502001 145.35 1502002 145.7 1502003 146.05 1502004 146.4 1502005 146.75 1502006 147.1 1502007 147.45 1502008 147.8 1502009 148.15 1502010 148.5 1502011 148.85 1502012 149.2 1502013 149.55 1502014 149.9 1502015 150.25 1502016 150.6 1502017 150.95 1502018 151.3 1502019 151.65 1502020 152 1502021 152.35 1502022 152.7 1502023 153.05 1502024 153.4 1502025 153.75 1502026 154.1 1502027 154.45 1502028 154.8 1502029 155.15 1502030 155.5 1502031 155.85 150

2032 156.2 1502033 156.55 1502034 156.9 1502035 157.25 1502036 157.6 1502037 157.95 1502038 158.3 1502039 158.65 1502040 159 1502041 159.35 1502042 159.7 1502043 160.05 1502044 160.4 1502045 160.75 1502046 161.1 1502047 161.45 1502048 161.8 1502049 162.15 1502050 162.5 1502051 162.85 1502052 163.2 1502053 163.55 1502054 163.9 1502055 164.25 1502056 164.6 1502057 164.95 1502058 165.3 1502059 165.65 1502060 166 1502061 166.35 1502062 166.7 1502063 167.05 1502064 167.4 1502065 167.75 1502066 168.1 1502067 168.45 1502068 168.8 1502069 169.15 1502070 169.5 1502071 169.85 1502072 170.2 1502073 170.55 1502074 170.9 1502075 171.25 1502076 171.6 150

2077 171.95 1502078 172.3 1502079 172.65 1502080 173 1502081 173.35 1502082 173.7 1502083 174.05 1502084 174.4 1502085 174.75 1502086 175.1 1502087 175.45 1502088 175.8 1502089 176.15 1502090 176.5 1502091 176.85 1502092 177.2 1502093 177.55 1502094 177.9 1502095 178.25 1502096 178.6 1502097 178.95 1502098 179.3 1502099 179.65 1502100 180 1502101 180.35 1502102 180.7 1502103 181.05 1502104 181.4 1502105 181.75 1502106 182.1 1502107 182.45 1502108 182.8 1502109 183.15 1502110 183.5 1502111 183.85 1502112 184.2 1502113 184.55 1502114 184.9 1502115 185.25 1502116 185.6 1502117 185.95 1502118 186.3 1502119 186.65 1502120 187 1502121 187.35 150

2122 187.7 1502123 188.05 1502124 188.4 1502125 188.75 1502126 189.1 1502127 189.45 1502128 189.8 1502129 190.15 1502130 190.5 1502131 190.85 1502132 191.2 1502133 191.55 1502134 191.9 1502135 192.25 1502136 192.6 1502137 192.95 1502138 193.3 1502139 193.65 1502140 194 1502141 194.35 1502142 194.7 1502143 195.05 1502144 195.4 1502145 195.75 1502146 196.1 1502147 196.45 1502148 196.8 1502149 197.15 1502150 197.5 1502151 197.85 1502152 198.2 1502153 198.55 1502154 198.9 1502155 199.25 1502156 199.6 1502157 199.95 1502158 200.3 1502159 200.65 1502160 201 1502161 201.35 1502162 201.7 1502163 202.05 1502164 202.4 1502165 202.75 1502166 203.1 150

2167 203.45 1502168 203.8 1502169 204.15 1502170 204.5 1502171 204.85 1502172 205.2 1502173 205.55 1502174 205.9 1502175 206.25 1502176 206.6 1502177 206.95 1502178 207.3 1502179 207.65 1502180 208 1502181 208.35 1502182 208.7 1502183 209.05 1502184 209.4 1502185 209.75 1502186 210.1 1502187 210.45 1502188 210.8 1502189 211.15 1502190 211.5 1502191 211.85 1502192 212.2 1502193 212.55 1502194 212.9 1502195 213.25 1502196 213.6 1502197 213.95 1502198 214.3 1502199 214.65 1502200 215 150

2014.2857114286 149.999999 150regular-exe cost= 0.00

Note: I equate cell ( D434) to 0 to automatically adjust "the mins required" in cell A433 using Excel Solver.

Julie will be indifferent about which plan to chose at the level where the expenses for both plans equal each other.At 1800 minutes , the regular plan cost a fixed price of $75 with $0.35 per additional minutes, while the executive plan cost $150 fixed price for 2200 with $0.30 per additional minutes. Therefore, the expenses for regular plan increases by $0.35 from 1800mins while the executive plan start increasing from 2200mins by $0.30.

That is, at 2200 minutes, the regular plan total expenses = $75 + (0.35 *(2200-1800))=$195, while the executive plan remain $150.Therefore, at 2200 mins, the regular plan is greater than the executive plan, but at 1800 minutes, it is less than the executive plan because it is $75, while excutive is $150.

Hence, it can be deduced that the level where the total expenses will be equal to each other is between 1800 and 2200minutes. And, at this point, the total expenses for executive plan remain $150.Therefore, regular plan total expenses = executive total expenses at < 2200minutes = $150.

Regular expenses = $75 + (0.35 *(X-1800) = $1500.35 *(X-1800) = 150-75 = 75X-1800 = 75/0.35 = 214.29X = 214.29 + 1800 = 2014.3Therefore, the volume level of minutes at which Julie would be indifferent between the two plan is approximately 2014 minutes or rounded to 2015 minutes to be able to enjoy the last 1minute fully.

Julie will be indifferent about which plan to chose at the level where the expenses for both plans equal each other.At 1800 minutes , the regular plan cost a fixed price of $75 with $0.35 per additional minutes, while the executive plan cost $150 fixed price for 2200 with $0.30 per additional minutes. Therefore, the expenses for regular plan increases by $0.35 from 1800mins while the executive plan start increasing from 2200mins by $0.30.

That is, at 2200 minutes, the regular plan total expenses = $75 + (0.35 *(2200-1800))=$195, while the executive plan remain $150.Therefore, at 2200 mins, the regular plan is greater than the executive plan, but at 1800 minutes, it is less than the executive plan because it is $75, while excutive is $150.

Hence, it can be deduced that the level where the total expenses will be equal to each other is between 1800 and 2200minutes. And, at this point, the total expenses for executive plan remain $150.Therefore, regular plan total expenses = executive total expenses at < 2200minutes = $150.

Regular expenses = $75 + (0.35 *(X-1800) = $1500.35 *(X-1800) = 150-75 = 75X-1800 = 75/0.35 = 214.29X = 214.29 + 1800 = 2014.3Therefore, the volume level of minutes at which Julie would be indifferent between the two plan is approximately 2014 minutes or rounded to 2015 minutes to be able to enjoy the last 1minute fully.

Julie should chose the executive plan because she will safe a cost of $105 on expenses ( i.e: 495-390).

QUESTION 2 A

Linear Programming model

X1 X2Decision Variable Product A Product B QuantityObjective Function Max 60A + 90B profitConstraints 6A + 10B <= 90hrs Assemble hrs availableConstraints 12A + 10B <= 125hrs Finishing hrs availableConstraints A + B <= 15 Units that available warehouse space can contain

QUESTION 3

X1 X2Decision Variable Valley Nectar Valley RedObjective Function Maximize 12000N + 15000RConstraints 6N + 9R <= 80 GrapeConstraints 5N + 5R <= 75 Storage spaceConstraints 15N + 10R <= 120 Processing timeConstraints N <= 8 Demand for Nectar Constraints R <= 8 Demand for Red