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kompoz [17]
2 years ago
14

A fast-food restaurant buys hamburger buns from a national bakery supplier. The daily usage of buns at the restaurant is normall

y distributed with an average of 160 and standard deviation of 10. It takes 4 days for the supplier to deliver. The purchasing agent at the restaurant has established a 99.7% service level.
a) The Safety Stock and Reorder Point for the restaurant (in whole numbers). A fast-food restaurant buys hamburger buns from a local bakery. To estimate its costs, the restaurant assumes now those buns are used at the constant rate of 100 per day and are purchased at $0.025 per bun. It costs $1 for each order placed and the annual inventory holding cost per unit is 25% of the unit purchase cost.
b) How much should be ordered each time to minimize the restaurant’s total annual costs?c) And what is the length of order cycles (i.e. time between orders) in days? Assume the restaurant operates 360 days per year.
Business
1 answer:
tekilochka [14]2 years ago
7 0

Answer:

Thus, from the calculations below;

The safety stock = 55

The reorder point = 695

quantity required to be ordered in order to reduce and minimize total annual cost for the restaurant = 3394 buns

The order cycles length = 34 days

Explanation:

From the given information:

The average demand (d) = 160

The standard deviatiion \sigma_d = 10

Lead time = 4 days

Service level = 99.7% = 0.997

From the Standard Normal Curve; the z value at 99.7% = 2.75

The annual demand (D) = 36000

Ordering cost = $1

Unit purchased Cost = $0.025

The holding cost for the annual inventory = 25% of 0.025 = 0.00625

The reorder point can be determined by using the formula:

= \bar d \times Lead \ time +z\times \sigma_d \times \sqrt{LT}

\mathbf{ = 160\ \times4+2.75 \times10 \times\sqrt{4}}

= 695

The safety stock SS = z \times \sigma_d \times \sqrt{LT}

= 2.75 \times 10 \times \sqrt{4}

= 55

The economic order quality = \sqrt{2 \times D \times \dfrac{ordering \ cost }{annua l\  holding \  cost}}

= \sqrt{2 \times 36000 \times \dfrac{1 }{0.00625}}

=3394.11

The order cycle length = \dfrac{EOQ}{D}\times 360

= \dfrac{3394.11}{36000}\times 360

= 33.94

≅ 34 days

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Answer:

Products         Selling price   Unit variable cost

                                $                       $

Junior                     50                      15

Adult                       75                      25

Expert                     <u>110 </u>                   <u> 60</u>

Total                      <u> 235 </u>                  <u> 100</u>

The sales price per composite unit = $235

The contribution margin per composite unit

= Composite selling price - Composite unit variable cost  

= $235 - $100

= $135

Break-even point in units

= <u>Fixed cost</u>

  Contribution per unit

= <u>$114,750</u>

  $135

= 850 units

Break-even point in dollars

= Break-even point in units x Composite selling price

= 850 units x $235

= $199,750

                     Income Statement    

                                                               $

Total contribution ($135 x 850 units)   114,750

Less: Fixed cost                                     <u>114,750</u>

Net profit                                                   <u> 0</u>

                                                                                                                                                                             

Explanation:

Sales price per composite unit is the aggregate of all the selling prices.

Contribution margin per composite unit equals composite selling price minus composite unit variable cost.

Break-even point in units is fixed cost divided per composite contribution margin per unit.

Break-even point in dollars equal break-even point in units multiplied by selling price.

Income statement is prepared by deducting the total fixed cost from the total contribution.

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