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Rack A holds 80 pairs of slacks with prices ranging from $12 to $15 a pair, and rack B holds 60 pairs of slacks with prices ranging from $13 to $18 a pair. If all the slacks are sold，what is the greatest amount by which the revenue the from the sale of slacks on rack A could possibly exceed the revenue from the sale of slacks on rack B?
A $430
B $412
C $122
D $120
E $112
A $430
B $412
C $122
D $120
E $112
thkkrpratik
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28 Apr 2022, 05:25
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Rack A holds 80 pairs of slacks with prices ranging from $12 to $15 a pair, and rack B holds 60 pairs of slacks with prices ranging from $13 to $18 a pair. If all the slacks are sold，what is the greatest amount by which the revenue the from the sale of slacks on rack A could possibly exceed the revenue from the sale of slacks on rack B?
A $430
B $412
C $122
D $120
E $112
A $430
B $412
C $122
D $120
E $112
For the maximum difference in revenue, we need the maximum possible revenue for rack A and the least possible revenue for rack B.
One caveat to consider is we are given a range of prices. So our price selections for the rack should fulfill that as well.
Max. revenue for Rack A
Maximum revenue = 79 x 15 + 1 x 12 (We take 1 slacks at $12 to fulfill the condition of range of prices)
= (80 x 15) - 15 + 12
(Changed the calculation values to make it easier to calculate)
= 1200 - 3
= $1197
Min. revenue for Rack A
Minimum revenue = 59 x 13 + 1 x 18 (We take 1 slacks at $18 to fulfill the condition of range of prices)
= (60 x 13) - 13 + 18
(Changed the calculation values to make it easier to calculate)
= 780 + 5
= $785
Difference = 1197 - 785
= $412
Option B
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