EL BOOZO, a gin importer, bottles three blends,

the Beafmonger, the Tanqued-Up and Vallantine's, sold at the respective prices

of $34, $28.50 and $22.50 per bottle. These blends are produced from

of three gins that the company imports, MODEL A gin, MODEL B gin

and gin type C. Although the market for these three gin blends is

very large, the EL-BOOZO company cannot import every month more than

than the quantities permitted by the import regulations. These

maximum quantities as well as the purchase prices of imported gins are

given in the table below

Imported Gin Imported Gin Maximum Quantity Purchase price per bottle

A 2700 35 $

B 3200 25 $

C 1900 20 $

The three mixtures are composed as follows:

- The Beafmonger must contain not less than 60% imported gin of the type

A, not more than 20% imported type C gin (no restriction on gin

imported type B in this mixture) ;

- The Tanqued-Up must contain not less than 15% imported gin of type

A, not more than 60% imported type C gin (no restrictions on gin

imported type B in this mixture) ;

- Vallantine's must contain no more than 50% imported gin type C

(no restriction on imported gins of type A and B in this blend).

A) Formulate the linear program model to help EL BOOZO to

Determine the quantity of each of the mixtures to be produced and the quantity to be produced composition to maximize contributions to profits and to the give the optimal solution.

B) Calculate for each of the mixtures the manufacturing cost by bottle for the most favourable composition for the importer.