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MAT 142 Calculus For Business And Social Science

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MAT 142 Calculus For Business And Social Science

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MAT 142 Calculus For Business And Social Science

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Course Code: MAT142
University: Montgomery County Community College is not sponsored or endorsed by this college or university

Country: United States

ABC Auto sells 600 new automobiles a year. It costs $300 to store one automobile for a year. To reorder automobiles there is a fixed cost of $80 for each time an order is placed and a cost per automobile of $50. How many automobiles must be ordered each time to minimize inventory costs?  How many orders must be made? What is the minimum cost?  You must use calculus and show a sufficient amount of work.

Let the number of automobiles orders per be represented by p
Let the number of automobiles per orders be represented by y  
We shall assume that any time an order is made, some vehicles are sold while others remain in the storage. We shall assume that the orders in the storage spend half the time before a reorder is done.
The reorder interval is  days
From the assumption made above, it can be implied that an automobile spends  days in the store.
The cost per day of storing an automobile will be 
The cost of storing an automobile for  days will be   
But we have 600 automobiles, hence total storage cost would be 
The cost of making a single order is 
If p number of orders are made, then the total costs for all orders in a year would be  
Hence, the total cost for p orders would be  
The total cost, R(y) would be a summation of all the costs. Therefore 
Differentiating the above equation with respect to y, we get 
The minimum is at a point when  
Number of orders to be done are 
The minimum total cost is given by 
But y= 18    
Works Cited
Kaplan, Wilfred. Maxima and Minima with Applications: Practical Optimization and Duality. New York: John Wiley & Sons, Inc., 2011.
Stewart, James. Calculus. 8th. Boston: Cengage Learning, 2016.

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