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 ​$10 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?
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Part 1
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
  
enter your response here.
The number of engines to send to plant II is
  
enter your response here.