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, 3201,320 hours of labor are available under a union agreement. The firm also has a stock of 2403,240 board feet of quality redwood. Each bench that Outdoor Furniture produces requires 88 ​labor-hours and 1212 board feet of​ redwood; each picnic table takes 66 ​labor-hours and 3030 board feet of redwood. Completed benches will yield a profit of ​$1010 ​each, and tables will result in a profit of $1515 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 produced equals= _____

​(round your response to the nearest whole​ number).

Number of tables

produced equals=_____

​(round your response to the nearest whole​ number).

Optimal solution value​ = _____

​(round your response to the nearest whole​ dollar).

Answer 1

This problem can be solved from excel solver. Since its not mentioned that its compulsory to build at least one of each type and also the optimal values can be whole number, we can assume that optimal number could be 0 also.

Here we need to maximize the profit we earn. Total redwood and labour force available is given and also amount required for each type.

Based on the optimal number we can calculate the amount of redwood and labour force that will be required to meet the number. This will lead us to the constraints for the LP program.

				Formulas Used
Total Profit (To be maximized)	2001820	$		D10*F7+D11*F8
Redwood Available	24,03,240	Board feet
Labour Force	32,01,320	hours
	Redwood reqd/unit	Labour force hours reqd/unit	Profit ($)/unit
Bench	1212	88	1010
Picnic Tables	3030	66	1515
Optimal units of Benches	1982
Optimal units of Tables	0
Total Redwood used	2402184			D10*D7+D11*D8
Total Labour hours used	174416			D10*E7+D11*E8

Below are the values in the solver :

Here we have taken the following constraints :

1. The optimal values of the benches and tables is a an integer type with value grater than or equal to 0

2. Total redwood used (optimal number of units*redwood needed for one unit) and similarly labour hour used should be less than equal to the total available values.

Based on the solver :

Number of benches produced equals= 1982

​(round your response to the nearest whole​ number).

Number of tables produced equals= 0

​(round your response to the nearest whole​ number).

Optimal solution value​ = $ 2001820

​(round your response to the nearest whole​ dollar).