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The Cream and Custard Bakery makes both coffee cakes and Danish in large pans. The main
ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available
and the maximum demand for coffee cakes is 8. Five pounds of flour and 2 pounds of sugar
are required to make one pan of coffee cake, and 5 pounds of flour and 4 pounds of sugar are
required to make one pan of Danish. One pan of coffee cake has a profit of PhP 1, and one pan
of Danish has a profit of PhP 5. Determine the number of pans of cake and Danish that the
bakery must produce each day so that profit will be maximized.
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This problem is simple: it is accessible to a third-grader.
Therefore, I will not write a standard solution using Linear programming method,
but will show a simple arithmetic solution.
From the problem, it is clear that the maximum number of cakes is 5.
Indeed, the bakery can make 5 coffee cakes, using 5*5 = 25 pounds of flour and 5*2 = 10 pounds of sugar.
It can not make more than 5 cakes, either coffee cakes or Danish.
So, our task is to make a schedule (a Table) showing possible cakes that can be prepared, and possible profit.
Obviously, we should spend as much of the ingredients as allowed by restrictions.
Also, from the given data, it is obvious, that for any given number of total cakes, the bakery should
make as many Danish pans as possible, then adding coffee cakes until fitting the restrictions.
It is because the first limiting restriction is the amount of floor, and regarding the floor,
the coffee cakes and the Danish pans are in equal position, while Danish provides greater profit.
the number coffee Danish Floor Sugar Profit
of cakes cakes pans (Php)
(total)
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5 5 0 5*5 = 25 5*2 = 10 5*1 = 5
4 0 4 0*5+4*5 = 20 0*2+4*4 = 16 4*5 = 20 (*)
4 1 3 1*5+3*5 = 20 1+3*5 = 16
4 2 2 2*5+2*5 = 20 2*2+2*4 = 12 2*2+2*4 = 12
There is no sense to continue the table further.
Looking into the table, we mark the optimum solution by (*).
It provides the maximum profit of Php 20 .
ANSWER. 4 Danish pans and 0 (zero) coffee cakes satisfy the restrictions and provide the maximum profit of Php 20.
Solved.