A furniture company manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 25,000 board feet of oak and 20,000 board feet of pine are available. A table requires either 17 board feet of oak or 30 board feet of pine, and a chair requires either 5 board feet of oak or 13 board feet of pine. Each table can be sold for $1000, and each chair for $300.

a. Determine how the company can maximize its revenue.

b. Use SolverTable to investigate the effects of simultaneous changes in the selling prices of the products. Specifically, see what happens to the total revenue when the selling prices of oak products change by a factor [tex]1+k_1[/tex] and the selling prices of pine products change by a factor [tex]1+k_2[/tex]. Revise your model from the previous problem so that you can use SolverTable to investigate changes in total revenue as [tex]k_1[/tex] and [tex]k_2[/tex] both vary from -0.3 to 0.3 in increments of 0.1. Can you conclude that total revenue changes linearly within this range?

To solve this problem and determine how the company can maximize its revenue, we can set up a linear programming model. Let's define the decision variables:

Let x be the number of tables to be produced.

Let y be the number of chairs to be produced.

The objective is to maximize the total revenue, which is given by:

Revenue = 1000x + 300y

We also need to consider the following constraints:

1. Availability of oak: 17x + 5y <= 25,000 (board feet)

2. Availability of pine: 30x + 13y <= 20,000 (board feet)

3. Non-negativity constraint: x >= 0, y >= 0 (number of tables and chairs cannot be negative)

Using Solver in Microsoft Excel or other optimization software, we can solve this linear programming problem and find the optimal values of x and y that maximize the total revenue.

Regarding part b of the question, to investigate the effects of simultaneous changes in the selling prices of the products, we can use SolverTable. We can set up a table where we vary the selling prices of oak and pine products by factors (1 + k1) and (1 + k2), respectively, within the range of -0.3 to 0.3 in increments of 0.1. For each combination of k1 and k2, we can use Solver to find the optimal values of x and y and calculate the corresponding total revenue.

By examining the results from SolverTable, we can observe the changes in total revenue as the selling prices vary and determine whether the changes follow a linear pattern within the given range.

Visit here to learn more about linear programming brainly.com/question/33171163

#SPJ11