A manufacturing company receives orders for engines from two aseembly plants. Pl

Question

A manufacturing company receives orders for engines from two aseembly 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. Plants I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant II gives similar $15 rebates. The mnufacturer 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, subject to the given constraints? ?

Thanks for help !!

Explanation / Answer

Hi..

The 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 rebates of $15. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. The shipping cost of the company has to be minimized..

From the information givens, the rebate given by Plant I is $20 and the shipping cost to send an item to this plant is $30. If the company supplies to Plant II, it only gets a rebate of $15 while the shipping cost is higher at $40.

To minimize shipping cost the company should send as many engines as it can to Plant I. If it is obliged to send at least 32 engines to Plant II, that should be done. The rebate received for this is 32*15 = 480. As the company requires a rebate of $1500, the remaining amount can be got if 51 engines are sent to Plant II. The total shipping costs incurred are 51*30 + 32*40 = $2810..

The company should send 32 engines to Plant II and 51 engines to Plant I.

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