Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice.
-How many constraints are required to model this as a linear program?
A) 8
B) 9
C) 10
D) 12

Question

Quizplus · Accepted Answer

There are 5 variables in the problem - x1, x2, x3, x4, x5.

The objective function is to maximize the profit:

maximize 2x1 + 4x2 + 3x3 + 5x4 + 6x5

The constraints are:

x1 + x2 + x3 + x4 + x5 ≤ 1000 (constraint on the total number of units of the product that can be produced) 
x1 ≤ 400 (constraint on the capacity of machine 1) 
x2 ≤ 250 (constraint on the capacity of machine 2) 
x3 ≤ 300 (constraint on the capacity of machine 3) 
x4 ≤ 200 (constraint on the capacity of machine 4) 
x5 ≤ 150 (constraint on the capacity of machine 5) 
x1, x2, x3, x4, x5 ≥ 0 (non-negativity constraints)

Therefore, there are a total of 10 constraints (6 inequality constraints and 4 non-negativity constraints) to model this as a linear program.

Companies A, B, and C Supply Components to Three Plants