Question

Bell Computers purchases integrated chips at ​$350 per chip. The holding cost is ​$35 per unit per​ year, the ordering cost is ​$119 per​ order, and sales are steady at 405 per month. The​ company's supplier, Rich Blue Chip​ Manufacturing, Inc., decides to offer price concessions in order to attract larger orders. The price structure is shown below. Rich Blue​ Chip's Price Structure Quantity Purchased ​ Price/Unit ​ 1-99 units ​$350 ​ 100-199 units ​$325 200 or more units ​$300 ​a) What is the most​ cost-effective order quantity and the minimum annual cost for Bell Computers to​ order, purchase, and hold these integrated​ chips, using the data and discount choices​ provided, and using a fixed holding​ cost? The most​ cost-effective order quantity​ (assuming they take the most​ cost-effective discount, and use a fixed holding​ cost) is nothing units ​(enter your response as a whole ​number). At the chosen level of quantity​ discount, and using the fixed holding​ cost, what is the total annual cost for Bell computers to​ order, purchase, and hold the integrated chips​ : ​$ nothing ​(round your response to the nearest whole​ number). ​b) Bell Computers wishes to recalculate using a 10​% holding cost rather than the fixed ​$35 holding cost in part a. What is the most​ cost-effective order​ quantity, and what is the corresponding annual​ cost? The most​ cost-effective order quantity​ (assuming they take the most​ cost-effective discount, and use a​ percentage-of-price holding​ cost) is nothing units ​(enter your response as a whole ​number). At the chosen level of quantity​ discount, and using the ​percentage-of-price holding​ cost, what is the total annual cost for Bell computers to​ order, purchase, and hold the integrated chips​ : ​$ nothing ​(round your response to the nearest whole​ number).

Answer 1

Answer:

When holding costs are $35 per unit,

1.The most cost-effective order quantity (assuming they take the most cost-effective discount, and use a fixed holding cost) is 182 units.

2. At the chosen level of quantity, discount, and using the fixed holding cost, the total annual cost for Bell computers to order, purchase, and hold the integrated chips is $1,585,898.

When holding costs are 10% of purchase price per unit,

1.The most cost-effective order quantity (assuming they take the most cost-effective discount, and use a fixed holding cost) is 189 units.

2. At the chosen level of quantity, discount, and using the fixed holding cost, the total annual cost for Bell computers to order, purchase, and hold the integrated chips is $1,585,546.

When holding costs are $35 per unit,

We follow these steps to arrive at the answer:

1. We have

Ordering Costs per order   $119

Holding Cost per unit            $35

Demand per month            405 units

Demand per year is                                $405*12 = 4860 units$

Since the most cost-effective order quantity is the Economic Order Quantity (EOQ), we compute the EOQ

$\mathbf{EOQ = \sqrt{\frac{2SD}{H}}}$

where

D is  demand per year

S is the Ordering cost per order

H is the holding cost per unit

Substituting the values we get,

$EOQ = \sqrt{\frac{2*(405*12)*119}{35}}$

$EOQ = \sqrt{33048}$

$\mathbf{EOQ = 181.7910889 \approx 182 units}$

2. The annual costs of ordering, purchasing and holding the integrated chips is the sum of the cost of ordering, purchasing and holding the integrated  chips.

Since the EOQ at 182 units falls in the second slab of Rich Blue Manufacturing, Bell computer can purchase chips at $325 per unit

Cost of purchasing the chips     $\mathbf{405*12*325 = 1579500}$

Number of orders to placed         $\frac{Annual Demand}{EOQ}$

Number of orders to placed         $\frac{405*12}{182}$

Number of orders to placed   $\mathbf{26.703 \approx 27 orders}$

Cost of orders                           $Number of orders * Cost per order$

Cost of orders                               $\mathbf{27 * 119 = 3213 }$

Holding Costs                        $\frac{EOQ}{2} * Holding cost per unit$

Holding Costs                               $\frac{182}{2} * 35$

Holding Costs                               $\mathbf{3185 }$

Total annual costs       $\mathbf{1579500 + 3213 + 3185 = 1585898}$

When holding costs are 10% of purchase price per unit,

1. We need to calculate the EOQ, which holding cost at each purchase price

$EOQ_{350} = (2*(405*12)*119)/(350*0.10) \approx 182 units$

$\mathbf{EOQ_{325} = (2*(405*12)*119)/(325*0.10)\approx 189 units}$

$EOQ_{300} = (2*(405*12)*119)/(300*0.10)\approx 197 units$

Since the EOQ lies between 100 and 199 units in all the three costs, Bell Computers can purchase the units only at $325 per unit, so its holding cost will be 10% of $325, which is $32.50 per unit.

2.2. The annual costs of ordering, purchasing and holding the integrated chips is the sum of the cost of ordering, purchasing and holding the integrated  chips.

Since the EOQ at 189 units falls in the second slab of Rich Blue Manufacturing, Bell computer can purchase chips at $325 per unit

Cost of purchasing the chips     $\mathbf{405*12*325 = 1579500}$

Number of orders to placed         $\frac{Annual Demand}{EOQ}$

Number of orders to placed         $\frac{405*12}{189}$

Number of orders to placed   $\mathbf{24.762 \approx 25 orders}$

Cost of orders                           $Number of orders * Cost per order$

Cost of orders                               $\mathbf{25 * 119 = 2975 }$

Holding Costs                        $\frac{EOQ}{2} * Holding cost per unit$

Holding Costs                               $\frac{189}{2} * 32.5$

Holding Costs                               $\mathbf{3071.25 }$

Total annual costs    $\mathbf{1579500 + 2975 + 3071.25 = 1585546.25 }$