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MIE 597SL Supply Chain Logistics Prof. Ana Muriel Homework #1 Part 1: AMPL Practice Problems Consider the example we worked on in the AMPL orientation videos: 3D Manufacturing Company must determine the mix of its 3D printers to be produced next year. The company produces two product lines, the Rogue and the Pro. • The average profit is $400 for each Rogue and $800 for each Pro. Fabrication and assembly are limited resources. • There is a maximum of 5,000 hours of fabrication capacity available per month (Each Rogue requires 3 hours and each Pro requires 5 hours). • There is a maximum of 3,000 hours of assembly capacity available per month (Each Rogue requires 1 hour and each Pro requires 4 hours). How many of each printer should be produced each month in order to maximize profit? Recall that we formulated the problem mathematically as Decision Variables: X1 = the number of Rogue produced each month X2 = the number of Pro produced each month Z = total monthly profit from Rogue and Pro Maximize Profit Z = 400 X1 +800 X2 Subject to: 3 𝑋1 + 5 𝑋2 ≤ 5000 𝑋1 + 4 𝑋2 ≤ 3000 𝑋1 , 𝑋2 ≥ 0 And we coded it in AMPL with model file GeneralModel.mod: reset; set I; /*set of products */ set J; /*set of resources */ param P{I}; /*Profit associated with product i*/ param R{I,J}; /*Amount of resource j required to produce one unit of product i */ param C{J}; /* Capacity available for resource j*/ var X{I} >=0; /* Number of units of product i produced*/ maximize profit: sum{i in I} P[i]*X[i]; subject to capacity {j in J}: sum{i in I} R[i,j]*X[i]

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