Question

DIRECTIONS: Solve the following problem using linear programming. A company manufactures two types of desks, the standard model and the deluxe model. Each standard model requires 2 hours of labor in the cutting department and 1 hour of labor in the assembly department. Each deluxe model requires 6 hours of labor in the cutting department and 2 hours of labor in the assembly department. The maximum working hours available per day in the cutting and assembly department are 180 and 70 , respectively. The company makes a profit of $120 on each standard model sold and $340 on each deluxe model. 1. How many of each type of desk should be produced and sold per day for the company to make maximum profit? 2. What is the maximum corresponding profit? 1st: Summarize the data provided by the problem in the following table: 2nd: Establish the system of linear inequalities that satisfy the conditions of the problem and the Objective Function. 3rd: Draw the graph of the system of inequalities (shade the feasible region). 4th: Determine the corner points and the value of the corresponding objective function (complete the table) 4th: Write the conclusion: Must be produced and sold daily luxury type so that the company makes maximum profit. The corresponding maximum gain is

Answer 1

To solve this linear programming problem, summarize the data in the table and establish a system of linear inequalities satisfying the constraints.

Denote the number of standard desks produced as "x" and the number of deluxe desks produced as "y". The constraints are: 2x + 6y ≤ 180 (cutting department constraint) and 1x + 2y ≤ 70 (assembly department constraint). The objective function represents the profit as profit = 120x + 340y.

Draw a graph of the system of inequalities and shade the feasible region, representing the combinations of x and y values that satisfy the constraints. Determine the corner points of the feasible region and evaluate the objective function at each corner point. Calculate the combination of x and y values that gives the maximum profit.

Conclusion: The company should produce and sell a certain number of deluxe desks per day to maximize its profit. The corresponding maximum gain is the value obtained from the objective function at the point that gives the highest profit.