Problema Solution
1. The Big Bang explosives company produces customized blasting compounds for use in the mining industry. The four ingredients for these explosives are agents A, B, C and D. Big Bang just received an order for 2000 pounds of explosive. Agents A and C each costs $5 per pound, agent B costs $6 per pound, and agent D costs $3 per pound. The customer's mixture must contain at least 20% agent A, at least 30% agent B, and at least 15% each for agents C and D. Additionally, the customer insists that there must be at least twice as much agent B as agent C in the mix and that the poundage of agent A must be at least 40% of what’s used for agent D. Finally, at least 200 pounds of each agent should be present in the finished product. The company wants to provide the least expensive mixture which will satisfy the customer’s requirements.
a) Formulate the LP model for this problem
b) What is the optimal solution?
c) How many pounds of each agent are used in the mix?
d) What is the total cost to mix the customer’s order?
Answer provided by our tutors
Let agents A, B, C and D weigh a, b, c and d pounds.
So the total cost is 5a+6b+5c+3d which is to be minimized.
Now, a+b+c+d = 2000.
The proportionality contstraints reduce to a >= 400, b >= 600, c >= 300 and d >= 300.
Customer requirements are b >= 2c, a >= 0.4d, a>=200, b>=200, c>=200 and d>=200.
So the LP model is
Minimize 5a+6b+5c+3d
subject to
a+b+c+d = 2000
b-2c >= 0
a-0.4d >= 0
a>400, b>600, c>300, d>300
Using excel solver, the optimal weight of agent A, B, C and D is 400, 600, 300 and 700 pounds respectively.
Total cost is $9200.