MATH 1630 Summer 2018 Homework: Section 3.3 Homework Save Score: 0.33 of 1 pt 3
ID: 1165204 • Letter: M
Question
MATH 1630 Summer 2018 Homework: Section 3.3 Homework Save Score: 0.33 of 1 pt 3 of 9 (4 complete) Hw Score: 25.93%, 2.33 & Bus Econ 3.3.7 Question Help 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 $50 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 I 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? How many engines should be shipped to each plant to minimize shipping costs, subject to the giver constraints? The number of engines to send to plant I is The number of engines to send to plant I is Enter your answer in the edit fields and then click Check Answer part Clear All Check AnswerExplanation / Answer
As the manufacture want to minimize the cost and the cost to send to plant II is high, so he will only send that many plants II that is atleast required.
It means the number of engines to send to plant II is 32 plants.
Now he also want rebates of atleast $1500.
So from plant II, he get 32*15 = $480 --- rebate
The required rebate = 1500 - 480 = $1020
This rebate will be cover by sending engines o plant I and each Plant I gives a rebate of $20.
so it requires $1020 / $20 = 51 enginees to send to plant I, so that the requirement of $1500 rebate could be managed.
the total enginee is also not exceed 140 i.e, 51+ 32 = 83 < 140.
It means, to minimize shipping costs, subject to given constraint.
The number of enginees to send to plant I = 51
The number of enginees to send to plant II = 32.
** this question could alao be done mathematically, but i assume that you might not know the concept, so i did it in the logical and simple manner, the answer is same from both the methods**.
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