Mrs. White wants to crochet beach hats and baby afghans for a church fund-raising bazaar. She needs 6 hours to make a hat and 3 hours to make an afghan and she has 60 hours available. She wants to make no more than 15 items and no more than 11 afghans. The bazaar will sell the hats for $19 each and the afghans for $8 each. How many of each should she make to maximize the income for the bazaar?
A) 5 hats and 10 afghans
B) 7 hats and 8 afghans
C) 11 hats and 4 afghans
D) 10 hats and 5 afghans
Answers
Given : needs 6 hours to make a hat and 3 hours to make an afghan and she has 60 hours available. She wants to make no more than 15 items and no more than 11 afghans. The bazaar will sell the hats for $19 each and the afghans for $8 each
To find : How many of each should she make to maximize the income for the bazaar
Solution:
6 hours to make a hat
3 hours to make an afghan
Let say number of Hats = H
& number of Afghans = A
H + A ≤ 15
A ≤ 11
6H + 3A ≤ 60
=> 2H + A ≤ 20
INCOME = 19H + 8A
HATS AFGAN HOURS INCOME
4 11 57 76 + 88 = 164
5 10 60 95 + 80 = 175
6 8 60 114 + 64 = 178
7 6 60 133 + 48 = 181
8 4 60 152 + 32 = 184
9 2 60 172 + 16 = 187
10 0 60 190
Maximum profit = 190 when 10 Hats only
out of given options only 5 hats and 10 afghans possible
as all other needs more than 60 hrs
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