Question

Problem 1. Model the following problem as an LP and solve it by the graphical method (a template is provided in Figure 2, next page). (40 points: 20 points modeling, 20 points solving) LightCo produces two types of lamps (type I and type II) that require metal parts and electrical components. Each lamp type I requires 1 unit of metal part, and 2 units of electrical components, and it can be sold for $1. Each lamp type II requires 3 units of metal parts and 2 units of electrical components, and it can be sold for $2. LightCo has 200 units of metal parts and 300 units of electrical components every day. There is no limit for the demand of lamp I, while the customer is not willing to buy more than 60 lamps of type II every day. The management team wants to maximize the profits of LightCo.

Answer 1

Let it Produces x number of type I lamps y number of type II lamps We need to maximize the total Profit, P constraints x+ 2y (Metal parts) (electrical components) (limit of type II) х+ Зу <- 200 2х + 2y - <= 300 y<= 60 150 100 2х +2y —300 (0, 60) (20, 60 y =60 50 (125, 25) feasible region X +3y_=200 100 200 (150, 0 Optimum solution occurs at corner points of feasible region. P 02*60 (0,60) (20,60) (125,25) (150,0) 120 P 202*60 = 140 P 125 2*25 = 175 = 150 P 150 0 Hence maximum profit at (125, 25). LightCo should produce 125 of type I lamps and 25 of type II lamps to maximize the profit.