"fashion furniture makes two kinds of chairs; rockers and recliners. two machinges a and b are used. machine a is limited to 20 hours per day. machine b is limited to 15 hours per day. machine a takes two hours to make each rocker and four hours to make each recliner. fashion furniture makes a profit of 12$ on each rocker and $10 on each recliner. how many of each type of chair should they make?"

Question

"fashion furniture makes two kinds of chairs; rockers and recliners. two machinges a and b are used. machine a is limited to 20 hours per day. machine b is limited to 15 hours per day. machine a takes two hours to make each rocker and four hours to make each recliner. fashion furniture makes a profit of 12$ on each rocker and $10 on each recliner. how many of each type of chair should they make?"

We're missing constraints for machine b.

Answer 1

To determine the number of rockers and recliners that Fashion Furniture should make, we need to consider the constraints of both machines A and B and optimize the profit.

Let's assume that machine B has a constraint of being limited to X hours per day. With this additional constraint, we can now solve the problem.

To find the optimal solution, we need to follow these steps:

Step 1: Define the variables:
Let's say R represents the number of rockers to be made.
Let's say C represents the number of recliners to be made.

Step 2: Set up the constraints:
From the information given in the problem statement, we have the following constraints:

Machine A: Can work for a maximum of 20 hours per day.
Machine B: Can work for a maximum of X hours per day.

Now let's establish the time constraints for each type of chair:

Rockers:
It takes 2 hours to make each rocker on machine A.

Recliners:
It takes 4 hours to make each recliner on machine A.

To summarize the time constraints we have:

2R + 4C ≤ 20 (for machine A)
X ≥ 0 (for machine B)

Step 3: Objective function:
We want to maximize the profit. The profit for each rocker is $12, and the profit for each recliner is $10. The total profit function is:

Profit function (P) = 12R + 10C

Step 4: Identify the feasible region:
We need to identify the feasible region by graphing the inequalities from the constraints established in Step 2.

Step 5: Optimize the objective function:
We need to find the maximum value of the profit function P = 12R + 10C within the feasible region identified in Step 4.

This optimization problem can be solved using linear programming techniques, such as the Simplex Method or graphical methods.

However, since we are missing the constraint for machine B, it is not possible to find the exact solution to the problem. We need additional information on the limitations of machine B to proceed further.