Question

The Outdoor Furniture Corporation manufactures two​ products, benches and picnic​ tables, for use in yards and parks. The firm has two main​ resources: its carpenters​ (labor force) and a supply of redwood for use in the furniture. During the next production​ cycle, 980 hours of labor are available under a union agreement. The firm also has a stock of 4,500 board feet of quality redwood. Each bench that Outdoor Furniture produces requires 4 labor-hours and 12 board feet of​ redwood; each picnic table takes 5 ​labor-hours and 25 board feet of redwood. Completed benches will yield a profit of ​$10 ​each, and tables will result in a profit of ​$15 each. How many benches and tables should Outdoor Furniture produce in order to obtain the largest possible​ profit?

The optimum solution​ is:

Number of benches produce =？ (round your response to the nearest whole​ number).

Number of tables=？​(round your response to the nearest whole​ number).

Optimal solution value​ = $？​(round your response to the nearest whole​ dollar).

Answer 1

Let no. of benches be B and no. of picnic tables be T

Total profit = 10B + 15T

We have to maximize this objective function

Subject to Constraints

4B + 5T <= 980..............Constraint for no. of labor hours available

12B + 25T <= 4500.........Constraint for board feet available

We solve the given LPP in Excel using Excel Solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

As seen from above,

The optimum solution​ is:

Number of benches produce = 50

Number of tables=156

Optimal solution value​ = $2840

----------------------------------------------------------------------------------------------------------------------------------------------------

In case of any doubt, please ask through the comment section before Upvote/downvote.