A manufacturing company makes two products(window air conditioners = X and centr
ID: 3260488 • Letter: A
Question
A manufacturing company makes two products(window air conditioners = X and central air units = Y). The profit estimates are $1000 for each unit of window unit sold and $1200 for each central air unit sold. The labor-hour requirements for the products in each of the three production departments are summarized below:
(hrs.)
Department A Department B Department C
Product X (window)
8
3
10
Product Y (central air)
12
3
5
The production supervisors in the departments have estimated that the following number of labor-hours will be available during the next month: 48 hours in department A, 18 hours in department B, and 40 hours in department C. Assuming that the company is interested in maximizing profits, formulate a linear program for this problem.
Max 1000X + 1200Y
s.t.
8x+12y<=48
3x+ 3y <=18
10x + 5y <=40
End
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 5400.000
VARIABLE VALUE REDUCED COST
X 3.000000 0.000000
Y 2.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
Dept A 0.000000 87.500000
Dept B 3.000000 0.000000
Dept C 0.000000 30.000000
Answer this question: If you had one more hour of employment time - in which department would you put the employee and why?
Department A and expect to make an additional $3.00
Department A and expect to make an additional $87.50
Department B and expect to make $3
Department C and expect to make an additional $30.50
(hrs.)
Department A Department B Department C
Product X (window)
8
3
10
Product Y (central air)
12
3
5
Explanation / Answer
Answer Option (b)
Explanation
Dual prices, also known as shadow prices, represent the worth of the resource represented by the variable.
In given solution, dual price of Dept A is 87.5 and that of Dept C is 30.0. This would imply that by using one additional unit of Dept A profit would be up by 87.5, whereas by using one additional unit of Dept C profit would be up by only 30.
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