Let:
x = number of tables to be made
y = number of desks to be made
A. The objective is to maximize the weekly profit, which is given by:
Profit = ($4/table) * x + ($3/desk) * y
Subject to the following constraints:
1. Labor constraint: 1 hour of labor is required to produce 1 table, and 3 hours are required to produce 1 desk. The total labor available is at most 45 hours. So, the constraint is:
1x + 3y ≤ 45
2. Wood constraint: 10 square feet of wood are required to produce 1 table, and 20 square feet are required to produce 1 desk. The total wood available is at most 350 square feet. So, the constraint is:
10x + 20y ≤ 350
3. Finish constraint: 2 quarts of finish are required to produce 1 table, and 1 quart is required to produce 1 desk. The total finish available is at most 55 quarts. So, the constraint is:
2x + y ≤ 55
4. Non-negativity constraint: The number of tables and desks cannot be negative. So, the constraints are:
x ≥ 0
y ≥ 0
B. To find the number of each product to be made in order to maximize the profit, we solve the linear programming problem using the given information and constraints. The optimal solution will give us the values of x and y that maximize the profit.
A firm manufactures tables and desks. To produce each table it requires 1 hour of labour, 10 square feet of wood, and 2 quarts of finish. To produce each desk it requires 3 hour of labour, 20 square feet of wood, and 1 quarts of finish. Available is at most 45 labour hours, at most 350 square feet of wood and at most 55 quarts of finish. The tables and desks yield profit of $4 and $3, respectively. Required
A. Formulate a linear programming problem that will maximize the weekly profit.
B. Find the number of each product to be made in order to maximize the profit.
1 answer
1 answer