# linear programming

posted by
**uma**
.

Brian Q’ Rourke, owner of The Horse & Hound Pub in Dublin, is preparing for St. Patricks Day, amd he must determine how much cider to stock. Brian sells three brands of cider on tap – Murphy’s Blackton, and red Rye. The cost per gallon (to the pub owner) of each brand is as follows:

Brand Cost/Unit

Murphy’s $1.50

Blackton 0.90

Red Rye 0.50

The pub budjet of $2,000 cider for St. Patricks Day. Brian sells Murphy’s at a rate $3.00 per gallon, Blackton at $2.50 per gallon and Red Rye at $1.75 per gallon. Based on previous St. Patrick’s Day celebrations, Brian has determined the maximum customer demand to be 400 gallons of Murphy’s, 500 gallons of Blackton, and 300 gallons of Red Rye. The pub has the capacity to stock 1,000 gallons of each brand of cider; Brian wants to stock completely. Brian wants to determine the number of gallons of each brands of cider to order in order to maximize profit.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.