Your Surf Shop sells two types of surfboards. The first, type A, costs $201 and you make a $22 profit on each one. The second, type B, costs $178 and you make a $16 profit on each one. You can order no more than 110 surfboards this month, and you need to make at least $1820 profit on them. If you must order at least one of each type of surfboard, how many of each type of surfboard should you order if you want to minimize your cost? a87 of type A23 of type B b23 of type A87 of type B c100 of type A10 of type B d10 of type A100 of type B
Question
Your Surf Shop sells two types of surfboards. The first, type A, costs 22 profit on each one. The second, type B, costs 16 profit on each one. You can order no more than 110 surfboards this month, and you need to make at least $1820 profit on them. If you must order at least one of each type of surfboard, how many of each type of surfboard should you order if you want to minimize your cost? a87 of type A23 of type B b23 of type A87 of type B c100 of type A10 of type B d10 of type A100 of type B
Solution
To solve this problem, we need to find the combination of surfboards that will give us the minimum cost while still meeting the profit requirement of $1820.
Let's denote the number of type A surfboards as 'a' and the number of type B surfboards as 'b'.
We know that:
- a + b ≤ 110 (we can't order more than 110 surfboards)
- 22a + 16b ≥ 1820 (we need to make at least $1820 profit)
We also know that we need to minimize the cost, which is 201a + 178b.
Let's start by checking each of the given options:
a) 87 of type A and 23 of type B This would give us a cost of 87201 + 23178 = 2142. This meets both the profit and quantity requirements.
b) 23 of type A and 87 of type B This would give us a cost of 23201 + 87178 = 1742. This does not meet the profit requirement.
c) 100 of type A and 10 of type B This would give us a cost of 100201 + 10178 = 2280. This meets both the profit and quantity requirements.
d) 10 of type A and 100 of type B This would give us a cost of 10201 + 100178 = 1680. This does not meet the profit requirement.
So, the options that meet both the profit and quantity requirements are a) and c). Between these two, option a) has a lower cost (20580), so the answer is a) 87 of type A and 23 of type B.
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