You have a chocolate factory, which produces dark chocolate and milk chocolate cake toppings. You wish to know how much of each type would be most profitable to produce. The profit from dark chocolate cake topping is the same as that for milk chocolate cake topping and is one dollar per kilo.

The two items, milk and cocoa, are needed to produce the chocolates. To produce a kilo of milk chocolate 2 liter of milk is needed and for a kilo of dark chocolate one liter of milk is needed and there is 10 liters of milk and 16 deciliters of cocoa available each day. To produce a kilo of dark chocolate 2 deciliters of cocoa is needed and for a kilo of milk chocolate a one decilitre of cocoa is needed. It has been decided that the amount of milk chocolate produced must not be more than 3 kilos greater than the amount of dark chocolate produced.

a) Can your variables be negative?

b) Write up the objective and constraints.

c) Draw the constraints and the polygon containing the feasible solutions.

d) Solve the problem and write the amount of dark chocolate and milk chocolate to be produced and the ?total profit with this production.

e) Change the profit to be 3 dollars for both products what is the amount produced of each product and ?what is the total profit achieved with this production.