Mat 142 Mathematics For The Assessment Answers

Answer:

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.