A company manufactures 3 types of parts which use precious metals, platinum and gold. Due to the shortage of these metals, the government regulates the amount that may be used per day. The relevant data with respect to supply, requirements and profit are summarized in the table below.
Product
Platinum
required/unit (gms)
Gold required/Unit
(gms)
Profit/unit
A
2
3
500
B
4
2
600
C
6
4
1200
Daily allotment of platinum and gold are 160 gm and 120 gm respectively. How should the company divide the supply of scarce precious metals? Formulate the linear programming model.
Let:
x = number of units of product A
y = number of units of product B
z = number of units of product C
The linear programming model can then be formulated as follows:
Objective function:
Maximize profit:
Profit = 500x + 600y + 1200z
Constraints:
Platinum constraint:
2x + 4y + 6z ≤ 160 (amount of platinum used should be less than or equal to the daily allotment of 160 gm)
Gold constraint:
3x + 2y + 4z ≤ 120 (amount of gold used should be less than or equal to the daily allotment of 120 gm)
Non-negativity constraints:
x ≥ 0
y ≥ 0
z ≥ 0
This linear programming model maximizes profit while considering the restrictions on the use of platinum and gold. The company should determine the optimal solution that maximizes profit within these constraints.