5.The Pinewood Furniture Company produces chairs and tables from two resources—labor and wood. The company has...

5.The Pinewood Furniture Company produces chairs and tables from two resources—labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day to maximize profit.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

Please solve in excel. Thanks

Solutions

Expert Solution

Let X1 be the number of produces chairs

and X2 be the number of produces tables

a) From the given information

	Labour	Wood	limit	Profit
Chairs	8	2	1	400
Tables	10	6		100
Availability	80	36	6

Formulation:

Objective function

Max Z = 400X1+ 100X2

Subject to Constraints

8X1 + 10X2 <=80 Labour constraint

2X1 + 6X2 <= 36 Wood Constraint

X1 <= 6

Non negative constraints

X1, X2 >=0

b) Graphical Method:

orchestra answered 1 year ago

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