The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of

Question

The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs S1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Shade Tolerance Traffic Resistance Drought Resistance2 Formulate a LP Model for this problem.

Explanation / Answer

Let Xa and Xb be the pounds of seed A and B in the blend respectively.

Minimize Z = Total cost = 1Xa + 2Xb
Subject to,
1Xa + 1Xb >= 300 (minimum shade tolerance)
2Xa + 1Xb >= 400 (minimum traffic tolerance)
2Xa + 5Xb >= 750 (minimum drought resistance)
Xa, Xb >= 0

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