On their farm, the Friendly family grows apples that they harvest each fall and make into three
products apple butter, applesauce, and apple jelly. They sell these three items at several local
grocery stores, at craft fairs in the region, and at their own Friendly Farm Pumpkin Festival for 2
weeks in October. Their three primary resources are cooking time in their kitchen, their own
labor time, and the apples. They have a total of 500 cooking hours available, and it requires 3.5
hours to cook a 10-gallon batch of apple butter, 5.2 hours to cook 10 gallons of applesauce, and
2.8 hours to cook 10 gallons of jelly. A 10-gallon batch of apple butter requires 1.2 hours of
labor, a batch of sauce takes 0.8 hour, and a batch of jelly requires 1.5 hours. The Friendly
family has 240 hours of labor available during the fall. They produce about 6,500 apples each
fall. A batch of apple butter requires 40 apples, a 10-gallon batch of applesauce requires 55
apples, and a batch of jelly requires 20 apples. After the products are canned, a batch of apple
butter will generate $190 in sales revenue, a batch of applesauce will generate a sales revenue of
$170, and a batch of jelly will generate sales revenue of $155. The Friendlys want to know how
many batches of apple butter, applesauce, and apple jelly to produce in order to maximize their
revenues.
To do:
Formulate a linear programming model for this problem. Solve the model by showing how this would be done on the computer.
Give the Objective function.
Give 4 constraints including nonnegative.
Showing working as if done on computer.