Question

The sales for a premium brand of coffee are 12,000 units monthly. It

costs the inventory manager $12 to place an order. The inventory
manager says that it costs $6 to store a jar Of coffee. The cost Of a jar Of
coffee is $20 and the average selling price is $44. What is value of R and Q?

Answer 1

The value of R is $0.25 and the value of Q is 48√(18,000).

Step-by-step explanation:

The value of R can be calculated using the formula:
R = (annual holding cost)/(annual demand)

To calculate the annual holding cost, we need to multiply the cost of storing a jar of coffee ($6) by the average number of units stored, which is half of the monthly sales (12,000/2 = 6,000).
Annual holding cost = $6 x 6,000 = $36,000

Next, we need to calculate the annual demand by multiplying the monthly sales (12,000) by 12 (since there are 12 months in a year).
Annual demand = 12,000 x 12 = 144,000

Therefore, R = $36,000/144,000 = $0.25

The value of Q can be calculated using the formula:
Q = √[(2 x N x S)/H]

Where:
N = Number of orders per year
S = Order cost per order
H = Holding cost per unit per year

To calculate the number of orders per year, we need to divide the annual demand (144,000) by the order quantity (Q).
N = 144,000/Q

Next, we can substitute the values of N and S into the formula to calculate Q.
Q = √[(2 x (144,000/Q) x $12)/$6] = √[(288,000/Q) x $2]

To solve for Q, we can square both sides of the equation and rearrange:
(Q^2)/288,000 = $2
Q^2 = $2 x 288,000
Q = √($2 x 288,000) = 12√(16 x 18,000)

Q = 12 x 4√(18,000) = 48√(18,000)

Therefore, Q = 48√(18,000)