To solve this problem using the graphical method, we can create a graph with the type A sheds on the x-axis and the type B sheds on the y-axis. The constraints can be represented as lines or inequalities on the graph.
1. Graph the constraints:
The first constraint is the machine time constraint: 2x + 3y ≤ 30, where x represents the number of type A sheds and y represents the number of type B sheds. This can be represented as a line on the graph: 2x + 3y = 30 or y = (30 - 2x)/3.
The second constraint is the craftsman time constraint: 5x + 5y ≤ 60, which can be represented as the line 5x + 5y = 60 or y = (60 - 5x)/5.
Additionally, we need to set the non-negativity constraints: x ≥ 0 and y ≥ 0.
2. Identify the feasible region:
The feasible region is the area on the graph that satisfies all the constraints. Shade this area on the graph.
3. Determine the objective function:
The profit function can be defined as P = 60x + 84y, where P represents the total profit.
4. Identify the highest profit point:
To maximize the total profit, we need to find the point within the feasible region that gives the highest profit. This can be done by calculating the profit at the vertices (corners) of the feasible region.
5. Evaluate the profit at the vertices:
To evaluate the profit at each vertex, plug in the x and y coordinates of each vertex into the profit function P = 60x + 84y.
6. Determine the vertex with the highest profit:
Choose the vertex with the highest profit, as this will give the maximum total profit. The corresponding values of x and y will be the optimal quantities of type A and type B sheds to build in order to maximize profit.
To solve this problem using the simplex tableau method, we would set up a linear programming problem with the constraints and objective function and use the simplex method to solve for the optimal solution. However, since the problem only involves two variables (x and y), it can be easily solved using the graphical method described above.
1, a small firm builds two types of garden shed. Type A requires 2 hours of machine time and 5 hours of crafts man time. Type B requires 3 hours of machine time and 5 hours of hours of crafts time.each day there are 30 hours of machine time available and 60 hours of crafts man time. The profit on each type A shed is 60 and on each type B shed is 84
A, use graphic method to determined how many garden shed of each type to build in order to maximize the total profit
B, use simplex tableau method to determined how many garden shed of each type to build in order to maximize the total profit
1 answer