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lesliejsantos lesliejsantos
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6 years ago
Gatson manufacturing company is willing to promote 2 types of tires: Economy tire and Premium tire. These two tires are independent of each other in terms of demand, cost, price, etc. An analytics team of this company has estimated the profit functions for both the tires as
   
 

Monthly profit for Economy tire = 49.2415 IN(XA) + 180.414
   
Monthly profit for Premium tire = 84.344 IN(XB) - 150.112


 


   where XA and XB are the advertising amount allocated to Economy tire and Premium tire, respectively, and IN is the natural logarithm function. The advertising budget is 200,000, and management has dictated that at least 20,000 must be allocated to each of the two tires.
 
   (Hint: To compute a natural logarithm for the value X in Excel, use the formula = IN(X). For Solver to find an answer, you also need to start with decision variable values greater than 0 in this problem.)


   
  Develop and solve an optimization model that will prescribe how the company should allocate its marketing budget to maximize profit.

Q. 2

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Q. 3

ukPKrPuAwFAx5dALZ4t0C9zrOxeHA 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

Q. 4

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

Q. 5

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

Q. 6

0O8KUSkLM5O1n3zki8xxMYU8fBXBe cnNC460Lckr4LtvScne/kPmO84hboNHl3tjyR7ypF9RbrOpRGKQcX8zETa+CxCOdePsbWiY0w+XKm1PRGDq7NbYdfSrbGlKvmprHWVitzM7VaebqmN+qXKpER7ixTAl1X3kVcUhpM4gsY3/xPdr5LWWd0WMLky7TW8jSIA8i9ULYnDuTYakWP0AuL0Yms71S6OIoWLYpS5F6sNmAVHty9huWD6llyfrrCsboX1t+OtvRkNSGZcwrjyL7ZPicOzTH7Uiw0zKUxBGJd57IoR5wuZtoguICJFcrCxckBJYr8jmKlneHasAtWvxJB9HQzejP7diiBYkWKsH0/KvWYgxuPX2D/uAb45efCKOFYFuXLWXKtdl6IS2E5D1CVH8qlR24jZ2dIFMLiBGw5uyyzXCwHocRLj/zYnp3fec5ORkYmH6BcCjETN2SPSQiZOtPDhypf9fEgJ0ol3qzYeh1FUNjqocvE2Zk8rdZ6kCVnJzOdDK3MWj+FkDMfzG0oa87OzDLnz1RrDcSJsMzKSaY06FWyjLpHjOltqU9hvgUooc3WY8mYrIFMrkrv2WniXcAIL28M2mltR24+LusHR3ab5H7VWCOeRj05P9bfJkKmSCjZmAJB2wfDscocPHznN1ll7hAkIesLRORNhHlDEZL/E883OTWV/BapJecnmSfRWJpsWmWETi425y4Vys0dlBixH1UVbE9YZpYpjRyjgLw9keMTS6SQMDk8RVKoyW9OI79fymyb3MfMvsXMvqXkrScpGXqyDamU3MfWfKCMMefSPjxyi70vZ2em5Tg8piv/NzTWClWB1yeBvMCJj7NjmZ6du+CfOYD9GUqThWKTlxOqzL6VDcBUeamPAjkdj5zK3sQMwi+Vp3+5o8om44ttmL9iPc5mGSrg06XjXsacRoNxKJa+i35JMSCnOTupFSgzGo3gklfkgKAg84c7au+YmB+P2LhYNhRqq/xjjc/jIDoshrytW4fP+LImEomQnJyMtAKWB5Tm7KRW4EyuUGLz1q1wdHQ0f7yi9q6VLY/y5cujXFkbZZ9iZcuhfMUKud/OR5iLi7lhwZOnzyAgQLd17e3VaM5OagXOWI+cx4N/YGDGByxq373xyDV9+foN1BoNYYnR5rW3V6M5O6kKpGiM3D7FtKZJsXihBUkfFSPPsdVKHhhttUKVH6KtVuxPBFbgJCSyHXkKmnLX/DAPjIKcKj9EQW5/oiDPFcht5+zkpOfqtLQx/5ZydlrEdM1VkR+fkTaKqqCIgtz+REH+mSDPMWcnAXYsJxFhYZEICA6DX1AY3obEIDxzj0+LZQV5KrQyS24+kRhSGZPz0txsSSRSIcn4AeAaU2HQa9+TNzGrEk4OQaN+Pjjo9211t6X68vp4kJuQqtdkyRnJ5JB9JwqbpIJUroA6Sw9fE9IMcnPTOJEECvXHxW7TknVQyZjehJYmdRJ1lhyWrFK1UMhlUOpSYOu2MOqYYXgV0GZJzmnfoiD/DJAzQLads1MKnkyMF5e2YZxHY7i5d4KHe2u0GDQfu29HQSKRZtmOGeRP2AFsmCEqd3VviapMUyKn0ij2B5Pz0pkdL6JKrTm4qbDdrTldktfYsqA/uu//uF4McQe6oXz7Htj+MucTQGWf+niQ63B3kQf+LFkKjpZ8laWK9sKWNzxL8uFkqMVcPNnQDeVcndB1W7AlZyeBuDoGF2e0gBNbnyujSaeNeJMtnyQDbR25ATPPDjwwFq3KlICDE7M/FzgUb41ZZwKhYZdJhY44O+HHxqJhhSKoN/sGLIMMZkjLw/6hJVDCpTwGHspxgBO7EwX5J4P8fTk7CcjlYjw6uhATh43FjgfEY48knnlYLPHI+R/2yKXmcRO4z9bCvWR9jD/8CrFkWiBUwjp8SrLKktVaKIbMOrBDqgGqwAuY4eOGhkvuQyhhsqVYivTKdC///9u78qimrjz8z/zTM07bqbUoBYG40NGqpS6DHhRUIgi4UBEQBY5YN1wQnXFBrdJWsS3gcSpFRKtDB9ei1g30uAKlRdRaFJQlhC1kIyGQhQSI39z7EiApwaHW9ozJ+875nZO8m3dfcs69X773e797P4VK27V/RHVGCN6dswAHi1gitzX0nciVuLDGDe4h23HxIS1ze4TU0BGwD01GsYyMpI487J7mgfmbE7BmsgNm7+10CNKivvwCPl16EMV0PBeewpp578AnpZjZ+6MTZVmbsGHpcmR17rFMUJg4G57cBUjJo9erw7nYKXDgrkHWYzrWK3Bo/lQExuxCLNcF3ptPo6rTEIWBGoIz6zF08kzMGDcQQenlNrNJG0vkz6nILXt2mhN5Wi4h8ko+KmoNpYZ92TSLQd03CB06Ax9fE5kMRD2U9dcR72PcUZDjigleCSho0aK54jziPOzxxut/xitvOmI4dzFS7+mh01TgbPwijKGfH2yPiVEJuCUx9MgSue3CjMif4dmpaW/GpdjxmBadgodG5Vt7NBjO0zbiPMOgZOxJxJAIC5EY4IK5XVZvRJG3a6HuVMuKIiRHjsfomGzy19CN8pOrsTwkDCdNPLnvJM2Fz/zV+M7ofdCaE4v3PcORdFtI3hnETmMLHxkRruD+gsi10lwkLnDDqq9OYIvPcIQeesISuQ3gN+fIe3p2dqdW1gR4YLrfLMzwCsCy+AzcqFJA0GDeR29ErucdQfAQb+zIrjWY3hLoGgvwacBIjFmfiWq6CIBfiPQoL4zySsRP7RooHn6HrSt8MGX3TQjpXsM6CXKzMpGScBUiat2Vl4wg3zlYceQRo4rqWCK3WZgRea+enWtxrISHKx95wGtRPLJLKMGXIC1sBGZsyQLP1LhRdQ+f+zv38Ox82tZCzqlHUdZm+A/xxOYcGRncbVArDHeVeQeWIDIwCAfu0b6laFbrULgvCFy/CKR9T4/V40wsmUdRe3BbYKrlRfhP+HBM32RC5O0K5CaGYuzW0+DzbmLXzCGYf5AlclvAbyJyi56d1EWfedhZi9LSMvxcVoP72WlYNy8U0ck5+FnejDqTPvpO5DpI8pIw0yUaJ8WduXI9am4mItx1IU7RtR2NRBVtDITPAYPzD/n6aG9VoUkiYSZuk+QqdvgtxJK4HNCtzhtYIrdZmBF5b56dTUpoO1pwZYsnhr3WH28zOWtn2L8+CquOF0NqspVye3NRTyLvkKM0YyU5hwOn4WPhvfMKET466KX3cXitO/Nn4Wj3Gl7t1w92zF753tiY8T1unF4NjzdehZ0jPcaBw5vOCN6TjUq697exa0CAb8yIvAPywv0IHx+Hc9QYWlmAXb4chHzdY2NzqwVL5C+cyCWo6Sw7FCkha3mMY9sjELk0CRfKWiESdvfRdyJXoy5zLVycN+KqSWWArOQYtnLHI+kReSPKx54Nc8BNMVqbPO2AruwSPlk4Ci5UYQ1zgt1fxiIy4SboT2aJ3HZhTuS9eHYqaGlqMy6v/zsmL9yJS8U0Zy2E+MonmPi36dh0gd91t2iRyCm0Cmb5uLA8F/ujfDBpTipK23VQNYmZ47dToxAxdx5Si2jfEsaazKDIw3Egnx5rgOhuGj4Y54GwL/Mh6WLybiJnnLTaHiEl0AXhiT+gWkLmZcm32OA1GLMSCyBWaGxClbNE/rxE3sOzsw6NMvK56jqUV9WBL5SjXqKCTFCA/esiEfWPI8itU0Eg6O7jVyny3CT4uqzCKWm3Iq++lYSIkRH4lha9CPOQEDuLELnB+QeqQuxdEIhxCw6ilCgsqeAitnGDsWQrq8htHX1PrVQiZ9skeEenoLirSvU2YjkDsSj5PqSdDNn6AMlmLvrkbrCtFeouzaFAwecLMXbEauSYDLeKPuTIgXJ8McUZ/tEn8KSrcEuK45Gu4MadQwP9Dk9zsXWkExydh2Io+e4cp0H46yt/Qr8BIzF13RkYf6lVgyXy5yBy5mFnD8/Oe6ioEeHO5Syk792FzKIalPEEyD35GaJCiGLPKESVvKnLePmZRF55GB84emLbpRqzHPnHfq54N+YYaskkFPHuIH2DP9yXnQBztuRHJC31xHvLj4MvlUNNJuje4NlwCz6ISjJxBde3Y+YARwRuv8
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wrote...
6 years ago
Ans. #1

Max 49.2415 IN(XA) + 180.414 + 84.344 IN(XB) - 150.112

s.t.
X
A + XB  200,000
X
A  20,000
X
B  20,000



The optimal solution is XA = 73,722.82 and XB = 126,277.18 with a profit of 1,572.93. The spreadsheet model follows:

Ans. #2



Ans. #3



Ans. #4



Ans. #5



Ans. #6

lesliejsantos Author
wrote...
6 years ago
Cheers!!
wrote...
6 years ago
Cheers too Thumbs Up Sign
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