A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular container costs the company $16, while the cylindrical container costs the company $15. If the company needs to
package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.
How many rectangular containers will be necessary to package 6,400 candles?
How many cylindrical containers will be necessary to package 6,400 candles?
Which container should the company use to minimize costs? Explain.

  a) no

  b) 143 rectangular containers

  c) 157 cylindrical containers

  d) both (preferring rectangular for the bulk of an order)

Step-by-step explanation:

a) If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs?

  No.*

For packaging 41 candles or fewer, the cylindrical container costs less than the rectangular one.

For packaging 6400 candles, there will be 10 candles left over if rectangular containers are used for most of the packaging needs. A dollar can be saved by packaging these remaining candles in a cylindrical container.

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b) How many rectangular containers will be necessary to package 6,400 candles?

  6400/45 = 142 10/45

If rectangular containers are used for all, then 143 are needed.

__

c) How many cylindrical containers will be necessary to package 6,400 candles?

  6400/41 = 156 4/41

If cylindrical containers are used for all, the 157 are needed.

__

d) Which container should the company use to minimize costs?

  The cost of 143 rectangular containers is 143×$16 = $2288

  The cost of 157 cylindrical containers is 157×$15 = $2355

  The cost of 142 rectangular and 1 cylindrical container is $2287

If only one shape container is used, the company should use rectangular containers to minimize cost. If either shape can be used, cost will be minimized by using one cylindrical container for the remnant of the order.

* This question is directed solely at the cost of materials required for packaging. We have advocated that both rectangular and cylindrical containers be made available. As a practical matter, the cost to the company of maintaining inventory of both sizes of containers may exceed the savings associated with using a cheaper container for smaller orders.

• 143

• 157

• the rectangular containers, because it will cost the company $67 more to use the cylindrical containers

Step-by-step explanation:

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step-by-step explanation: