Question

You are subcontracting 3 vendors. Vendor 1 charges $45 per unit and can supply the required quantity in four days. Vendor 2 charges $65 per unit and can supply the required quantity in two days. Vendor 3 charges $50 per unit and can supply the required quantity in three days. The organization's policy states that you cannot order more than 40% of your requirements to any one vendor. (Hint: Quantity ordered on any one vendor has to be less than equal to 40% of the total quantity subcontracted). The total budget you have for subcontracting is $300,000. Formulate a linear programming model that minimizes the total time taken to complete the deliveries.

1. What are the Decision Variables?

2. What is the Objective Function?

3. What are the constraints?

Answer 1

Answer a- The decision variables are given below=

x1= total quantities ordered to vendor 1

x2= total quantities ordered to vendor 2

x3= total quantities ordered to vendor 3

Answer b= The objective function is to minimize the total time in receiving the total number of required quantities

Min Z=4x1+2x2+3x3

Answer C= The constrains are as below=

x1$\leqslant$0.4(x1+x2+x3)

x2$\leqslant$0.4(x1+x2+x3)

x3$\leqslant$0.4(x1+x2+x3)

45x1+65x2+50x3 $\leqslant$ 300000

x1,x2,x3$\geqslant$0

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