Understood Parenthesis, Minimize Cost, Finding when increasing at greatest rate

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April 4th 2009, 04:22 PM
Jonboy

Understood Parenthesis, Minimize Cost, Finding when increasing at greatest rate

Hey everyone! I'd greatly appreciate some thoughts on these problems. Thanks in advance. (Rofl)

1) Inventory Cost.The cost of inventory depends on the ordering and storage costs according to the inventory model:

$C = \bigg(\frac{Q}{x}\bigg)s + \bigg(\frac{x}{2}\bigg)r$

Determine the order size that will minimize the cost, assuming that sales occur at a constant rate, Q is the number of units sold per year, r is the cost of storing one unit for 1 year, s is the cost of placing an order, and x is the number of units per order.

I have never found the minimum with so many variables. Can someone give me as starting point and I'll follow onward?

2) Modeling Data. The manager of a store recorded the annual sale S (in thousand of dollars) of a product over a period of 7 years, as show in the table, where t is the time in years, with t = 1 corresponding to 1991.

t....(1)......(2)......(3)........(4).....(5)....( 6).....(7)
S...(5.4)..(6.9)....(11.5)...(15.5)..(19)...(22).. .(23.6)

I was supposed to find a cubic function regression function and I did. But then one part says:

Use calculus to find the time when sale were increasing at the greatest.

Does this mean find the absolute maximum?
April 4th 2009, 04:57 PM
DeMath

Quote:

Originally Posted by Jonboy

Hey everyone! I'd greatly appreciate some thoughts on these problems. Thanks in advance. (Rofl)

1) Inventory Cost.The cost of inventory depends on the ordering and storage costs according to the inventory model:

$C = \bigg(\frac{Q}{x}\bigg)s + \bigg(\frac{x}{2}\bigg)r$

Determine the order size that will minimize the cost, assuming that sales occur at a constant rate, Q is the number of units sold per year, r is the cost of storing one unit for 1 year, s is the cost of placing an order, and x is the number of units per order.

I have never found the minimum with so many variables. Can someone give me as starting point and I'll follow onward?

This problem is known as the Wilson EOQ Model.

Look in the Wikipedia Economic order quantity
April 5th 2009, 05:57 AM
Jonboy

thanks Demath, i'll give that a try.

can someone give me some help on number 2 ? thank you!
April 5th 2009, 06:48 AM
DeMath

Quote:

Originally Posted by Jonboy

Hey everyone! I'd greatly appreciate some thoughts on these problems. Thanks in advance. (Rofl)

2) Modeling Data. The manager of a store recorded the annual sale S (in thousand of dollars) of a product over a period of 7 years, as show in the table, where t is the time in years, with t = 1 corresponding to 1991.

t....(1)......(2)......(3)........(4).....(5)....( 6).....(7)
S...(5.4)..(6.9)....(11.5)...(15.5)..(19)...(22).. .(23.6)

I was supposed to find a cubic function regression function and I did. But then one part says:

Use calculus to find the time when sale were increasing at the greatest.

Does this mean find the absolute maximum?

I think you just need to find the derivative of a cubic parabola, which you calculated, and then calculate the value of thise derivative in each of the 7 points [(5.4)..(6.9)....(11.5)...(15.5)..(19)...(22)...(23 .6)]. The largest of these values is the time when sale were increasing at the greatest.

What is the equation of a cubic parabola you got?