Question

Normal Nos Heading t Heading 2 No Spacing QS: The company produces two products (X1 and X2), which sells at $500 (for XI) and $450 (for X2) per unit. To produce XI requires 6 units of labor and 10 units of capital. To produce X2 requires 5 and 20 units of capital. If the available labor is 60 Units and available capital is 150 units, and the maximum storage capacity for XI is 8 units. (a) Formulate a linear programming problem for the company that maximize profit (b) Use the graphical approach to solve the problem by showing all optimal solution and valve of the vertexes on the feasible solutions. (c) Solve the problem using Microsoft Escel and submit your answers on Moodle (Missed Exam MacBook Air P11 8 5 3

Answer 1

a)

maximize
Z = 500 x1 + 450 x2

constraints

6x1 + 5 x2 <= 60
10 x1 + 20 x2 <= 150

x <= 8

b)

12 The value of the function at each of these extreme points is as follows Extreme Point Coordinates (x1ぬ) Objective function value Lines through Extreme Point 2-500x,+450x 50000) +450(0) 0 500(8) 450(0) 4000 5→x220 A(8, 0) 1→6x1 + 5x2 60 12 sooo»-.so(12).soso C(45부) l+6x1 + 5x2 2 → 10x1 +20x2 60 150 30、36000 150 2 → 10x1+20, 15 15 500(0) 3375 450 45 30 The maximum value of the objective function z occurs at the extreme point 30 36000 45 Hence, the optimal solution to the given LP problem is : x1-T x2-T and max:-T