This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
To find the maximum profit, we need to use the method of linear programming. Step 1: Define the objective function and constraints. Let x be the number of type A bicycles and y be the number of type B bicycles. The profit for a type A bicycle is K10 000, and for a type B bicycle is K15 000. The objective function to maximize profit P is: P = 10000x + 15000y From the previous part, the constraints are: 1. Cost constraint: 3x + 4y 120 2. Storage constraint: x + y 40 3. Non-negativity: x 0 4. Non-negativity: y 0 Step 2: Identify the vertices of the feasible region. The feasible region is defined by the intersection of these inequalities. We find the corner points (vertices) of this region. Intersection of x=0 and y=0: (0,0) Intersection of y=0 and 3x + 4y = 120: 3x + 4(0) = 120 3x = 120 x = 40. Vertex: (40,0) Intersection of x=0 and 3x + 4y = 120: 3(0) + 4y = 120 4y = 120 y = 30. Vertex: (0,30) Intersection of x + y = 40 and 3x + 4y = 120: From x + y = 40, we can write x = 40 - y. Substitute this into the second equation: 3(40 - y) + 4y = 120 120 - 3y + 4y = 120 120 + y = 120 y = 0 Substitute y=0 back into x = 40 - y: x = 40 - 0 = 40. Vertex: (40,0) The constraint x+y 40 is redundant because the feasible region is already bounded by $3x+