Question

Must Solve Using Graphical method and substitution

A company is producing two types of furniture. Product A requires9 board feet of wood and 3 lbs of wicker. Product B requires 7 board feet of wood and 5 lbs of wicker. There are 6000 board feet of wood available for the product and 2000 lbs of wicker. The time to assemble product A is 2.8 hours and product B is 5.0 hours. You have no more than 880 hours planned for production. The company has order equal to 50 units of product B. Product A earns a profit margin of $45 a unit and Product B earns a profit margin of $52 a unit.

In the space provided, write the objective function and the constraints.

Solve it using the graphical and substitution method.

a. What is the value of the objective function?

b. What is the value of Product A?

c. What is the value of product B?

d. If the company finds more hours for production, should they use them?

Round your answers to 2 decimal points.

Answer 1

Product	A	B
Decision variables	225	50
Profit	45	52
Wood	9	7
Wicker	3	5
Time	2.8	5
Objective Function	=	12725
Constraints
Wood	2375	<=	6000
Wicker	925	<=	2000
Time	880	<=	880
Product B >= 50	50	>=	50

a) Value of objective function is 12725

b) Value of product A is 225

c) Value of product b is 50

d)

		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coefficient	Increase	Decrease
$F$4	Decision variables A	225	0	45	1E+30	15.88
$G$4	Decision variables B	50	0	52	28.35714286	1E+30
		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$F$13	Wood =	2375	0	6000	1E+30	3625
$F$14	Wicker =	925	0	2000	1E+30	1075
$F$15	Time =	880	16.07142857	880	1003.333333	630
$F$16	Product B >= 50 =	50	-28.35714286	50	126	50

Since the shadow price for time is 16.07, it means that optimal value from object function will increase by 16.07 for each unit of hour increases.