Question

The DC Desk Company manufactures two types of computer desks from laminated particle board. The Senior Geek model requires 30 square feet of particle board, 1 keyboard sliding tray and 5 hours of labor to fabricate. This model has a net profit of $105. The Jr. Geek model requires 24 square feet of particle board, 1 keyboard sliding tray and 3 hours of labor to fabricate. The Jr. Geek model has a net profit of $95. During the next production cycle, the company can buy up to 15,000 square feet of particle board and up to 600 keyboard sliding trays. The company has 3000 hours of labor available during the next production cycle. The company has a limit of 450 of Jr. Geek desks it can make, and due to backorders must make at least 125 Senior Geek desks. The company wants to maximize profit.

Please Use Excel

Answer 1

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The DC Desk Company
Profit per labor hour	Senior Geek	Junior Geek	Note
Profit per unit ($)	105.00	95.00	A
Labor hour per unit	5.00	3.00	B
Profit per labor hour	21.00	31.67	C=A/B
Rank	2	1
Profit per square feet	Senior Geek	Junior Geek	Note
Profit per unit ($)	105.00	95.00	See A
Square feet per unit	30.00	24.00	D
Profit per square feet	3.50	3.96	E=A/D
Rank	2	1

For optimal utilization of resources that product will be produced first whose contribution per unit of resource is highest.

In this case contribution per labor hour and per square feet for Junior Geek is more. So it should be produced first and then remaining resources will be allocated to Senior Geek.

Production plan	Labor Hour	Board	Tray	Note
Input required per unit of Junior Geek	3.00	24.00	1.00	D
Maximum demand	450.00	450.00	450.00	E
Resource allocated	1,350.00	10,800.00	450.00	F=D*E
Maximum availability	3,000.00	15,000.00	600.00	H
Remaining Resource	1,650.00	4,200.00	150.00	I=F-H
Input required per unit of Senior Geek	5.00	30.00	1.00	J
Units to be produced of Senior Geek	330.00	140.00	150.00	K=I/J
So maximum units that can be produced from Senior Geek is 140.
Income Statement	Senior Geek	Junior Geek	Total
Profit per unit ($)	105.00	95.00		See A
Number of units	140.00	450.00		L= See E,K
Profit ($)	14,700.00	42,750.00	57,450.00	M=A*L
So maximum profit the company can earn is $ 57,450.