A specialist bakery makes two types of cakes, chocolate and fruit: Each chocolate cake uses 600 grams of flour, 100 grams of butter and 200 grams of sugar: The corresponding figures for a fruit cake are 300 grams, 100 grams and 300 grams. The bakery makes a profit of $20 and S24 for each chocolate and fruit cake sold: The bakery wants to make as many cakes of each type that it can to maximise total profit: However; it only has 9 kg flour; 20 kg butter and 52 kg sugar available each week You may assume that there are no other restrictions and that the bakery can sell all cakes that it makes. (a) Give a precise description of the two decision variables, x andy_ (b) Write down an expression in terms of x and y for the weekly profit: (c) Write down inequalities for all constraints in the problem. (d) Draw the feasible region and identify the coordinates of all of its corners_ (e) How many cakes of each type should be baked each week to maximise profit?

# A specialist bakery makes two types of cakes, chocolate and fruit: Each chocolate cake uses 600 grams of flour, 100 grams of butter and 200 grams of sugar: The corresponding figures for a fruit cake are 300 grams, 100 grams and 300 grams. The bakery makes a profit of $20 and S24 for each chocolate and fruit cake sold: The bakery wants to make as many cakes of each type that it can to maximise total profit: However; it only has 9 kg flour; 20 kg butter and 52 kg sugar available each week You may assume that there are no other restrictions and that the bakery can sell all cakes that it makes. (a) Give a precise description of the two decision variables, x andy_ (b) Write down an expression in terms of x and y for the weekly profit: (c) Write down inequalities for all constraints in the problem. (d) Draw the feasible region and identify the coordinates of all of its corners_ (e) How many cakes of each type should be baked each week to maximise profit?

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