Question

Question-3 (32 marks) (ASW-2016-14E-C2-TB52) 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 $1 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 then: (a) Model the problem as a Linear Program (b) Solve the linear program using the graphical method learned in the course (c) How many pounds of each seed should be in the optimal blend? Which targets will be exceeded? How much will the blend cost? Type A Type B 300 Shade Tolerance Traffic Resistance 2 Drought Resistance 2 5 750 1 x=TYPCA Х2= ТУfe B Eloo

Answer 1

Let A = the pounds of Type A seed in the blend
Let B = the pounds of Type B seed in the blend
Min 1A + 2B
s.t. 1A + 1B ≥ 300
2A + 1B ≥ 400
2A + 5B ≥ 750
A, B ≥ 0

Graphical Representation:

Solving we get,

A= 250

B=50

250 pounds of Type A seed, and 50 pounds of Type B seed should be in the blend.

Constraint 2 has a surplus value of 150, so theTraffic Resistance target is exceeded by 150.

The blend cost will be $350 as:

250 Pounds X $1 + 50 Pounds X $2 = 250+100 = $350.