Consider the all-units quantity discount schedule below. Which of the following sets of order quantities is guaranteed to contain the optimal solution (i.e., best order quantity)?
A) {1, 500, 1000, 1500, 2000}
B) {952, 986, 1023,1087, 1166}
C) {986, 1000, 1500, 2000}
D) {1023, 1500, 2000}
E) {986, 1023, 1500}

Question

Consider the all-units quantity discount schedule below.  Which of the following sets of order quantities is guaranteed to contain the optimal solution (i.e., best order quantity)?
A) {1, 500, 1000, 1500, 2000} 
B) {952, 986, 1023,1087, 1166} 
C) {986, 1000, 1500, 2000} 
D) {1023, 1500, 2000} 
E) {986, 1023, 1500}

Quizplus · Accepted Answer

The optimal solution occurs at the point where the marginal cost (price * discount) equals the marginal benefit (holding cost). Using the given schedule, we can calculate the marginal costs and benefit for each order quantity. Among the answer choices, only {1023, 1500, 2000} contains quantities where the marginal cost equals the marginal benefit, and no other answer choice contains all of these quantities. Therefore, D is the best choice.

Consider the All-Units Quantity Discount Schedule Below