An Electrical Company has two manufacturing plants. The cost in dollars of producing an Amplifier at each of the two plants is given below. The cost of producing Q1 Amplifiers at first plant is:
65Q1 + 4Q12+ 90
and the cost of producing Q2 Amplifiers at the second plant is
20Q2 + 2Q22+ 120
The company needs to manufacture at least 60 Amplifiers to meet the received orders. How many Amplifiers should be produced at each of the plant to minimize the total production cost? Round the answers to two decimal places and the total cost to the nearest dollar value.
If Q1 and Q2 are the number of units of amplifiers manufactured in first and second plant, respectively, then the optimization model is
Min (65Q1 + 4Q12+ 90) + (20Q2 + 2Q22+ 120)
s.t.
Q1 + Q2 ³ 60
Q1, Q2 ³ 0
The optimal solution to this model is to produce 16.25 Amplifier’s at plant 1 for a production cost of $2,202.50 and 43.75 Amplifier’s at plant 2 for a production cost of $4823.13. The total cost is $7026. The spreadsheet model follows.
Business
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