A company has decided to produce a new cereal called nuts and bran which contains only nuts and bran. It is to be sold in the standard size pack which must contain at least 375g. To provide an acceptable nutritional balance, each pack should contain at least 200g of bran. To satisfy the marketing manager, at least 20% of the cereal’s weight should come from nuts. The production manager has advised you that nuts will cost 20 cents per 100g and that bran will cost 8 cents per 100g. 

REQUIRED: 

1. Formulate a linear programming model for the minimization of costs. 

2. Solve your linear programming model graphically. 

3. Determine the cost of producing each packet of cereal.