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adoni [48]
2 years ago
13

What other considerations do manufacturers have when deciding on the dimensions of the cans, besides minimizing the amount of ma

terial used
Business
1 answer:
asambeis [7]2 years ago
8 0

Answer:

Imagine that you are an engineer for a soda company, and you are tasked with finding the most economical shape for its aluminum cans. You are given a set of constraints: the can ust hold a volume V of liquid and be a cylindrical shape of height h and radius r, and you need to minimize the cost of the metal required to make the can.

(a) First, ignore any waste material that is discarded during the manufacturing process and just minimuze the total surface area for a given volume V. Using this constraint, show that the optimal dimensions are achieved when h = 2t.

(b) Next, take the manufacturing process into account. Materials for the cans are fut from flat sheets of metal. The cylindrical sides ar made form curved rectangles, and rectangles can be cut from sheets of metal with virtually no waste. However, when the disks of the top and bottom of the can are cut from flat sheets of metal, there is significant waste material. Assume that the disks are cut from squares with side lengths of 2r, so that one disk is cut out of each square in a grid. Show that in this case the amount of material is minimized when: h÷r = 8÷π ≈2.55 .

(c) It is far more efficient to cut the disks from a tiling of hexagons than from a tiling of squares, as the former leaves far less waste material. Show that if the disks for the lids and bases of the cans are cut from a tiling of hexagons, the optimal ratio is h ÷ r = 4√3 ÷ π ≈ 2.21 . Hint: The formula for the area of a hexagon circumscribing a circle of radius r is A = 6r ^2 ÷ √3.

(d) Look at a variety of aluminum cans of different sizes from the supermarket. Which models from problems a-c best approximate the shapes of the cans? Are the cans actually perfect cylinders? Are there other assumptions about the maufacture of the cans that we should take into account? Do a little bit of research, and write a response to answer some of these questions by comparing our models to the actual dimensions used.

Explanation:

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Answer:

DM Cost per Equivalent unit: 4.25

Explanation:

22400 beginning  60% materials 20% conversion

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DM 71,160

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MO 20,110

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22,400 * .4     8,960

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DM Cost per Equivalent unit: 4.25

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3 years ago
Freda's Florist reported the following before-tax income statement items for the year ended December 31, 2021: Operating income
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Answer:

$63,750 and $80,500, respectively.

Explanation:

Operating income : 255,000 x 0.25   =  63,750

Discontinued:   67,000 x   0.25 =    16,750

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Rogen Corporation manufactures a single product. The standard cost per unit of product is shown below.
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Answer:

1. Material cost variance                            $

Standard material cost ($6  x  4,300)  25,800

Less: Actual ,aterial cost                       27,900

Material cost variance                            2,100(A)

2. Material price variance

= (Standard price - Actual price) x Actual quantity purchased

= ($6 - $6.20) x 4,500 pounds

= $900( A)

Actual price

=  Actual material cost/Actual quantity purchased

Actual price

= $27,900/4,500 pounds = $6.20

3. Material usage variance

= (Standard quantity - Actual quantity used) x Standard price

= (1 x 4,300 - 4,500) x $6

= $1,200(A)

4. Labour cost variance:                           $

Standard labour cost ($18.30 x 4,300)   78,690

Less: Actual labour cost                          77,500

Labour cost variance                                1,190

5. Labour rate variance

=(Standard rate - Actual rate) x Actual hours worked

= ($12.20 - $12.40) x 6,250 hours

= $1,250(A)

6. Labour efficiency variance

= (Standard hours - actual hours worked) x Standard rate

= (1.50 hours x 4,300 - 6,250) x $12.20

= $2,440(F)

Actual rate = Actual labour cost/Actual hours worked

Actual rate = $77,500/6,250 hours

Actual rate = $12.40

= (SR - AR) x Actual hour worked

7. Total overhead variance                                  $

 Standard overhead cost ($24 x 4,300)          103,200

Less: Actual overhead cost(78,430+ 26,670)  105,100

Total overhead variance                                     1,900

Less: Actual overhead cost

Explanation:

Material cost variance is the difference between standard material cost and actual material cost.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

Material price variance is the difference between standard price and actual price multiplied by actual quantity purchased.

Material usage variance is the difference between standard quantity and actual quantity used multiplied by standard price.

Labour cost variance is the difference between standard labour cost and actual labour cost.

Labour rate variance is the difference between standard rate and actual rate multiplied by actual hours worked.

Labour efficiency variance is the difference between standard hours and actual hours worked multiplied by standard rate.

Total overhead variance is the difference between standard total overhead cost and actual total overhead cost.

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