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?
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?
Solution
This problem can be solved using linear programming.
Let's denote the number of type A surfboards as x and the number of type B surfboards as y.
We have the following constraints:
- x + y ≤ 110 (You can order no more than 110 surfboards)
- 22x + 16y ≥ 1820 (You need to make at least $1820 profit)
- x ≥ 1 (You must order at least one type A surfboard)
- y ≥ 1 (You must order at least one type B surfboard)
The objective function to minimize is the total cost, which is 201x + 178y.
To solve this problem, you can graph the feasible region defined by the constraints and find the minimum of the objective function within this region.
Alternatively, you can use a linear programming solver to find the optimal solution.
Please note that the solution may not be an integer, in which case you would round to the nearest integer that satisfies all constraints.
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