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 $24 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 96 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 and y.
(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?