Let the number of white shirts be
m, and the number of blue shirts be
n. Hence, the total cost of the shirts =
(1000m+1125n), and the number of shirts is
(m+n)The average price of the shirts is
. It is given that he set a fixed market price which was
25% higher than the average cost of all the shirts. He sold all the shirts at a discount of
10%.
Hence, the average selling price of the shirts
The average profit of the shirts
The total profit of the shirts
Now,
⇒(1000m+1125n)=51000⇒1000m+1125n=51000×8=408000 Now to get the maximum number of shirts, we need to minimize
n (since the coefficient of
n is greater than the coefficient of
m ), but it can't be zero. Therefore,
m has to be maximum.
m=The maximum value of
m such that
m, and both are integers is
m=399, and
n=8 (by inspection)
Hence, the maximum number of shirts
=m+n=399+8=407