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andreev551 [17]
2 years ago
7

The Home and Garden (HG) chain of superstores imports decorative planters from Italy. Demand for the planters is stable and aver

ages at 150/week. Each planter costs $10. HG incurs a holding cost of 30% per year to carry inventory. HG has an opportunity to set up a superstore in the Phoenix region. Each order shipped from Italy incurs a fixed transportation and delivery cost of $5000. Consider 50 weeks in the year. Suppose HG uses the economic order quantity (EOQ) model to make ordering decisions. Then the average inventory that HG carries for the year would be
Business
1 answer:
Korolek [52]2 years ago
6 0

Answer:

The average inventory which HG should carry during the year is 5,000 units.

Explanation:

Economic Order Quantity is the ideal inventory procurement which minimizes holding and ordering cost. The EOQ is used by businesses in order to determine the best possible inventory holding.

EOQ = \sqrt{\frac{2*Annual Demand * Ordering Cost}{Annual Holding Cost} }

EOQ = \sqrt\frac{2*7,500*5,000}{10*0.3}

EOQ = 5,000 units

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You are given the market demand function Q=2800-1000p, and that each duopoly firm's marginal cost is $0.07 per unit, which impli
Fed [463]

Answer:

q1 = 910

q2 = 910

Explanation:

Given:

Q = 2800 - 1000p

Marginal cost = $0.07 per unit

Q = 2800 - 1000p

p = \frac{2800 - Q}{1000}

p = \frac{2800- q_1 - q_2}{1000}

Let's calculate profit of firm 1:

TR = p1 q1

= \frac{2800 q_1 - q_1^2 - q_1 q_2}{1000}

MR = \frac{2800 - 2q_1 - q_2}{1000}

MR = MC = 0.07

\frac{2800 - 2q_1 - q_2}{1000} = 0.07

Cross multiplying:

2800 - 2q₁ - q₂ = 70

2800 - 2q₁ = 70 + q₂

2800 - 70 - 2q₁ = q₂

2730 - 2q₁ = q₂...............(1)

Let's calculate profit of firm 2:

TR = p₁ q₂

= \frac{2800 q_2 - q_1 - q_2^2}{1000}

\frac{2800 - q_1 - 2q_2}{1000} = MR

MR = MC = 0.07

\frac{2800 - q_1 - 2q_2}{1000} = 0.07

Cross multiplying:

2800 - q₁ - 2q₂ = 70

2800 - 2q₂ = 70 + q₁

2800 - 70 - 2q₂ = q₁

2730 - 2q₂ = q₁................... (2)

Substitute 2730 - 2q₂ for q₁ in (1)...

Thus:

2730 - 2q₁ = q₂

2730 - 2(2730 - 2q₂) = q₂

2730 - 5460 + 4q₂ = q₂

-2730 + 4q₂ = q₂

-2730 = q₂ - 4q₂

-2730 = - 3q₂

q₂ = -2730/-3

q₂ = 910

Substituting 910 for q₂ in (2):

2730 - 2q₂ = q₁

2730 - 2(910)= q₁

2730 - 1820 = q₁

910 = q₁

q₁ = 910

The Cournot equilibrium quantities are: q₁= 910; and q₂ = 910

3 0
3 years ago
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