Question

Mikaya furniture shop located in pangasinan makes two kinds of products, cabinets (X1) and dresser(X2) which pas through the assembly and the finishing departments. the assembly department has a maximum of 60 hours finishing department has at most 48 hours each week. making one cabinet need 2 hours to finish and 4 hours to assemble while takes 2 hours to finish it. if the profit generated per cabinet is 1000.00 and per dresser is 800.00, how many units of cabinets and dressers should be produced in order to obtain the maximum, profit?

Answer 1

The student's question is about solving a linear programming problem to maximize profit for a furniture shop with given constraints on assembly and finishing department hours. Cabinets and dressers production is limited by the available hours, and the objective is to find the optimal number of each to maximize profit.

Step-by-step explanation:

The problem presented is an optimization problem, specifically linear programming, which can be solved using methods such as the graphical method or the simplex method for maximizing profit given a set of constraints. Let's designate cabinets by X1 and dressers by X2. According to the given constraints:

• Each cabinet (X1) requires 4 hours for assembly and 2 hours for the finishing department.
• Each dresser (X2) takes 1 hour to assemble and also 2 hours to finish.
• The assembly department has at most 60 hours available.
• The finishing department has at most 48 hours available.
• The profit for each cabinet (X1) is PHP 1,000.
• The profit for each dresser (X2) is PHP 800.

To obtain the maximum profit, we set up our constraints as follows:

• 4X1 + X2 ≤ 60 (assembly department constraint)
• 2X1 + 2X2 ≤ 48 (finishing department constraint)

And our objective function, which we want to maximize, is:

Profit = 1000X1 + 800X2

The solution to this problem will give us the number of cabinets and dressers to produce for maximizing profit, subject to the constraints on department hours.