Question

A trucking firm has a current capacity of 200,000 cubic feet. A large manufacturer is willing to purchase the entire capacity at $0.10 per cubic foot per day. The manager at the trucking firm has observed that on the spot market, trucking capacity sells for an average of $0.13 per cubic foot per day. Demand, however, is not guaranteed at this price. The manager forecasts daily demand on the spot market to be normally distributed, with a mean of 60,000 cubic feet and a standard deviation of 20,000 cubic feet. How much trucking capacity should the manager save for the spot market

Answer 1

The Manager should save 45,223 cubic feet of capacity for the spot market.

Step-by-step explanation:

Solution

Let us consider the following information:

The bulk contract cost, cb is 0.10 per cubic foot per day

$0.13 per cubic foot per day

The mean demand μ = 60,000

Standard deviation σ = 20,000

The current capacity is 200,000 cubic feet

Now,

let us determine the optimal value by applying the formula shown below.

p = cs- cb/ cs ------(1)

Let also calculate the trucking capacity that should be saved for the spot market

Q =NORMINV (p, μ,σ )------(2)

Thus, we substitute the values in the equation (1) given below:

cs = 0.13, cb =0.10

p =0.13-0.10/0.13

=0.03/0.13

=0.23

Now, substitute the obtained value of p in equation (2) with μ = 60,000 and σ = 20,000

Q = NORMINV (0.23, 60,000, 20,000)

= NORMINV (0.23, 60,000, 20,000

= 45223.06

= 45,223

Therefore the Manager should save 45,223 cubic feet of capacity for the spot market.