The Hickory Furniture Co. produces sofas and chairs. Their plant uses three main resources to make...

The Hickory Furniture Co. produces sofas and chairs. Their plant uses three main resources to make furniture –wood, upholstery and labor. The resource requirements and profits for each piece of furniture and the total resources available weekly are as follows:

	Sofa	Chair	Available Resource
Wood (lbs)	7	4	1200
Upholstery (yds)	12	0	600
Labor (hrs)	6	10	400

Profit	$500	$400

LINEAR PROGRAMMING (Hickory Furniture)

__________ 1a. How many sofas should be produced?
__________ 1b. How many chairs should be produced?
__________ 1c. How much profit will be earned optimally?
__________ 1d. What is the value of an additional hour of labor to the total profit?
__________ 1e. How much would the profit increase with an additional yard of upholstery?

__________ 1f. How much of the 1200 lbs of wood are actually used in the optimal solution?

__________ 1g. What is the lowest profit for sofas that would have the same optimal solution?

__________ 1h. What is the highest profit for chairs that would have the same optimal solution?

Expert Solution

1a. 50

1b. 10

1c. 29000

1d. Additional hour of labor makes no difference to profit as we have used up all hours, so we need minimum 6 hours additional to be able to produce 1 additional quantity.

1e. Additional yard makes no difference to profit as we have used up all yards, so we need minimum 12 yards additional to be able to produce 1 additional quantity or don't need any yards at all.

1f. 390 lbs of wood has been used

milcah answered 8 months ago

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