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.