Question

SOLVE THE FOLLOWING 2 LINEAR PROGRAMMING PROBLEMS USING EXCEL AND THE SOLVER ADD-IN.

PROBLEM #1:   Maximize Z = $60X + $90Y

                            Subject to:   60X + 30Y >= 1,500

                                                    100X + 100Y <= 6,000

                                                                             Y >= 30

                                                                          X, Y >= 0

PROBLEM #2: Minimize Z = $3,000X + $1,000Y

                             Subject to:   60X + 20Y >= 1,200

                                                        10X + 10Y >= 400

                                                     40X + 160Y >= 2,400

                                                                         X, Y >= 0

Answer 1

PROBLEM #1:   Maximize Z = $60X + $90Y

                            Subject to:   60X + 30Y >= 1,500

                                                    100X + 100Y <= 6,000

                                                                             Y >= 30

                                                                          X, Y >= 0

Inequalities	60x + 30y >=1500	100x +100y<=6000	Y>=30
Correspondent equation	60x + 30y =1500	100x +100y=6000	Y=30
Intersaction of lines with in X	(25,0)	(60,0)	(0,0)
Intersaction of lines with in	(0,30)	(0,60)	(0,30)

A (25,0) :- (60*25)+(90*0) = 1500

C (60,0):- (60*60)+(90*0)= 3600

Z is Maximum at 3600 point C (60,0) hance X is 60 and Y is 0

340,30) s * 25,0) (6010) 0 5 10 15 20 25 30 35 40 45 50 55 60 1570 Gox toy => 1oox Hooy-6000 oo)

PROBLEM #2: Minimize Z = $3,000X + $1,000Y

                             Subject to:   60X + 20Y >= 1,200

                                                        10X + 10Y >= 400

                                                     40X + 160Y >= 2,400

                                                                         X, Y >= 0

Inequalities	60x + 20y >=1200	10x +10y<=400	40x + 150y>=2400
Correspondent equation	60x + 20y =1200	10x +10y=400	40x + 150y=2400
Intersaction of lines with in X	(20,0)	(40,0)	(60,0)
Intersaction of lines with in	(0,60)	(0,40)	(0,15)

Analyzing cornor points A(20,0), C(40,0) & E(60,0)

A (20,0) :- (3000*20)+(1000*0) = 60000

C (40,0):- (3000*40)+(1000*0)= 120000

E(60,0):- (3000*60)+(1000*0)= 180000

so, Z is minimum at 60000 at A (20,0) hance X is 20, and Y is 0.

35+ 307 2$ 7 (60,0) 5 10 15 20 25 30 35 God so 58 60 65 70 10,0) lox tloy-160 yot 160=2400 Gox+20171200