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EleoNora [17]
3 years ago
8

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?
Mathematics
1 answer:
brilliants [131]3 years ago
6 0
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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3 years ago
A 8-foot tall man is standing beside a 32-foot flagpole. The flagpole is
kipiarov [429]

Answer:

The flagpole's shadow is 16.875 feet longer than the man's shadow

Step-by-step explanation:

The total length of the shadow is expressed by taking its actual length by a factor that depends on the position of the sun which is constant for the man too. The expression is as follows;

Height of the shadow=actual height of the flagpole×factor

where;

length of the flagpole's shadow=22.5 feet

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replacing;

length of man's shadow=8×0.703125=5.625 feet

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The flagpole's shadow is 16.875 feet longer than the man's shadow

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