A. To formulate a linear programming problem, we need to define the decision variables, the objective function, and the constraints.
Let x = number of type A doors produced
Let y = number of type B doors produced
The objective function is to maximize the weekly profit:
Maximize: 20x + 15y
The constraints are:
1. Production capacity constraint: 5x + 3y ≤ 500
2. Demand constraint for door A: x ≤ 70
3. Demand constraint for door B: y ≤ 125
4. Non-negativity constraint: x ≥ 0, y ≥ 0
B. To find the number of each type of garage doors manufactured to maximize the weekly profit, and the maximum profit, we need to solve the linear programming problem.
The maximum profit can be found by maximizing the objective function: 20x + 15y.
Subject to the constraints:
5x + 3y ≤ 500
x ≤ 70
y ≤ 125
x ≥ 0
y ≥ 0
After solving the linear programming problem, we will obtain the values of x and y that maximize the objective function. These values will represent the number of each type of garage doors manufactured.
The maximum profit will be the value obtained by plugging the values of x and y into the objective function: 20x + 15y.
A company makes two types of garage doors, type A and type B. Profit per unit is $20 for type A door and $15 for type B door. Both doors are produced in the same production process that has a total capacity of 500 labour-hours per week. The time required to make each unit is 5 hours for type A door and 3 hours for type B door. The maximum demand in a week for door A is 70 units while for door B is 125 units. Required
A. Formulate a linear programming problem that will maximize the weekly profit.
B. What is the number of each type of garage doors manufactured to maximize the weekly profit? What is the maximum profit?
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