4. * Christine and Tim are planning for a wedding reception at Logan Ridge, an u

Question

4. * Christine and Tim are planning for a wedding reception at Logan Ridge, an upstate winery overlooking one of the Finger Lakes. Since the invited guests have not replied on time, they are uncertain about the actual number of guests that will be attending the reception. To the best of the couple's knowledge, the number of guests will be normally distributed with the mean 170 and the standard deviation 20. A manager at Logan Ridge requests the couple for an estimate for the number of guests in order to prepare food. He guarantees that he will prepare food for 10 servings more than the estimate, and will charge based on the higher of the estimate and the actual number of guests. In an unfortunate case that a guest cannot be served, the goodwill cost will be 10 times the per-person charge. Christine and Tim need to provide an estimate for the manager at Logan Ridge. (a) Write down an appropriate objective function for the decision that Christine and Tim need to make. (b) What is the optimal solution? Use Excel if necessary.

Explanation / Answer

(a) The objective function for the decision that Christine and Tine need to make is what estimate to give for number of guests to the manager at Logan Ridge.

(b) Overage cost, Co = x (per person charge)

Underage cost, Cu = 10x (goodwill cost of a guest not being served)

Critical ratio = Cu/(Cu+Co) = 10x/(10x+x) = 10/11 = 0.91

Corresponding z value = NORMSIN(0.91) = 1.34

Optimal number of servings to prepare = Mean + z * Std dev = 170 + 1.34*20 = 197

The manager has assured that he will prepare 10 servings more than estimate. Therefore, estimate should be 10 less than the optimal number of servings to prepare

Estimate that Christine and Time should give = 197-10 = 187 guests

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.