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A manufacturing company receives orders for engines

04/10/2021 Client: muhammad11 Deadline: 2 Day

A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 ​engines, and plant II needs at least 32 engines. The company can send at most 140 engines to these assembly plants. It costs $30 per engine to ship to plant I and ​$40 per engine to ship to plant II. Plant I gives the manufacturing company ​$20 in rebates toward its products for each engine they​buy, while plant II gives similar ​$15 rebates. The manufacturer estimates that they need at least ​$1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping​costs? What is the minimum​ cost?

a.) How many engines should be shipped to each plant to minimize shipping​ costs, subject to the given​ constraints?

The number of engines to send to plant I is ____.

The number of engines to send to plant II is ____.

b.) What is the minimum shipping cost, subject to the given constraints?

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