Give and Take Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker $4\mathrm{.}5$ ?hours to assemble, a bologna sandwich requires $4\mathrm{.}1$ ?hours, and a chicken salad sandwich requires $5\mathrm{.}0$ ?hours to make. The company has $48$ ?available hours each night for sandwich assembly. Vending machine capacity is available for $2,000$ ?sandwiches each day. The profit for a ham and cheese sandwich is GH $?3\mathrm{.}5,$ ?the profit for a bologna sandwich is GH $?4\mathrm{.}2,$ ?and the profit for a chicken salad sandwich is GH $?3\mathrm{.}7.$ ?The company knows from past sales records that its customers buy as many or more of the ham and cheese sandwiches than the other two sandwiches combined, but customers need a variety of sandwiches available, so Metro stocks at most $200$ ?of each.

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ANSWER THE FOLLOWING QUESTIONS. LEAVE YOUR ANSWERS TO $2$ ?DECIMAL PLACES WHERE DECIMALS ARE REQUIRED.

$1.$ ?What is your optimal recommendation for sandwiches to offer subject resource constraints? Blank $1.$ ?Fill in the blank, read surrounding text.

? $,$ ? Blank $2.$ ?Fill in the blank, read surrounding text.

? $,$ ? Blank $3.$ ?Fill in the blank, read surrounding text.

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$2.$ ?Based on your recommendation which sandwich will you consider as profitable? Blank $4.$ ?Fill in the blank, read surrounding text.

$3.$ ?What is the profit for your recommendation in Q $2.?$ ? Blank $5.$ ?Fill in the blank, read surrounding text.

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$4.$ ?By how much profit will Give and Take likely to ascertain for the optimal mix. Blank $6.$ ?Fill in the blank, read surrounding text.

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$5.$ ?What is the minimum capacity required for vending machine for full utilisation? Blank $7.$ ?Fill in the blank, read surrounding text.

$6.$ ?Compute the maximum assembly time in hours require for production. Blank $8.$ ?Fill in the blank, read surrounding text.

$7.$ ?By how much extra profit will be attained for every $3$ ?hours assembly time introduced. Blank $9.$ ?Fill in the blank, read surrounding text.

$8.$ ?What will be the implication if Give and Take decide to decrease unit sales for Cheese by $10$ ?cedis? Blank $10.$ ?Fill in the blank, read surrounding text.

? $,$ ? Blank $11.$ ?Fill in the blank, read surrounding text.

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$9.$ ?What is the maximum unit sales required for Cheese sandwich? Blank $12.$ ?Fill in the blank, read surrounding text.

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$10.$ ?What is the shadow price for sales records given that past sales shows customers buy as many or more of the ham and cheese sandwiches than the other two sandwiches combined