A manufacturing company makes two products(window air conditioners = X and centr
ID: 3260481 • 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.
What should Pat produce for the optimal product selection?
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
Answer this question using this output.
A .Pat should make 2 window unit and 2 central air units for an expected profit of $4400.
b. Pat should make 3 window unit and 2 central air units for an expected profit of $4500.
c. Pat should make 2 window unit and 3 central air units for an expected profit of $5400.
d. Pat should make 3 window unit and 2 central air units for an expected profit of $5400.
(hrs.)
Department A Department B Department C
Product X (window)
8
3
10
Product Y (central air)
12
3
5
Explanation / Answer
The profit estimates are $1000 for each unit of window unit sold and $1200 for each central air unit sold.
so, the total expected profit = 1000 * X + 1200 * Y ; if X units of window unit sold and Y unit of central air unit is sold.
Now labour time is given for each of these product and departments , considering those constraints we construct the above mentioned LPP and the outcome is
Max Expected Profit = 5400
X = 3 and Y = 2
i.e Pat should make 3 window unit and 2 central air unit for an expected profit of 5400 given the constraints!
So your answer is (d)
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