Question

A 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 below. Type I seed costs $3.20 per pound and Type II seed costs $4.30 per pound. If the blend needs to score at least 600 points for shade tolerance, 650 points for traffic resistance, and 900 points for drought resistance, how many pounds of each seed should be in the blend? The garden shop wants to minimize total cost of production.

	Type I	Type II
Shade Tolerance	1.8	1.6
Traffic Resistance	2.3	1.3
Drought Resistance	3.6	4.5

Formulate a linear programming model for the above situation by determining

(a) The decision variables

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.

Answer 1

(a) Decision variables: Let x1 and x2 be the pounds of Type I and Type II grass seed to blend

(b) Objective function: MIN 3.2X1 + 4.3X2  

It represents the total cost of production.

(c) Constraints:

1.8X1+1.6X2 >= 600   (Shade tolerance)

2.3X1+1.3X2 >= 650   (Traffic resistance)

3.6X1+4.5X2 >= 900   (Drought resistance)

X1, X2 >= 0