Your surf shop sells two types of surfboards. the first type a, costs $272 and you make a profit of $29 on each one. the second type b costs $136 and you make a profit of $17 on each one. you can order no more than 50 surfboards this month, and you need to make at least $1210 profit on them. if you mush 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?

Let the number of type A surfboards to be ordered be x and the number of type B surfboards be y, then we have

Minimize: C = 272x + 136y

subject to: 29x + 17y ≥ 1210
                 x + y ≤ 50
                 x, y ≥ 1

From the graph of the constraints, we have that the corner points are:

(20, 30), (41.138, 1) and (49, 1)

Applying the corner poits to the objective function, we have

For (20, 30): C = 272(20) + 136(30) = 5440 + 4080 = $9,520
For (41.138, 1): C = 272(41.138) + 136 = 11189.54 + 136 = $11,325.54
For (49, 1): C = 272(49) + 136 = 13328 + 136 = $13,464

Therefore, for minimum cost, 20 type A surfboards and 30 type B surfboards should be ordered.

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