1998examfinal-soln

# 1998examfinal-soln - IE 221 OPERATIONS RESEARCH...

This preview shows pages 1–2. Sign up to view the full content.

IE 221 OPERATIONS RESEARCH / PROBABILISTIC MODELS FINAL EXAM SOLUTIONS , FALL 1998 1 . .. (a) production cost per dozen = (0.15)(12) = 1.8 price per dozen = (0.35)(12) = 4.2 “salvage” price per dozen = (0.05)(12) = 0.6 q = # dozens cookies baked daily d = \$ dozens cookies demanded daily d < q : cost = -4.2d + 1.8q – 0.6(q – d) = 1.2q – 3.6d c 0 = 1.2 d > q : cost = -4.2d + 1.8q = -2.4q c u = 1.2 F(q*) c u / (c o + c u ) = 2.4 / 3.6 = 0.667 q* = 40 dozens (b) P ( z (q* – 50) / 20 ) = 0.667 z* = 0.43 q* = 50 + (0.43)(20) = 58.6 dozen 2 . .. (a) EOQ = (2KE(D) / h) = (2(100)(5000) / 2) = 707.1 P ( X 80 ) = 1 – P ( z (r – E(X)) / σ X ) = 1 – P ( z (80 – 20) / 30 ) = 1 – 0.9772 = 0.0228 P ( X r* ) = hq* / (c B E(D)) 0.0221 = (2)(707.1) / (c B 5000) c B = 12.41 (shortage cost) [ Also, “shortage cost” = (D/Q) c B NL(z*) = (5000 / 707.1)(12.41)(0.0085) = 0.75 / year ] (b) 0.0228 = (2)(707.1) / [ 2(707.1) + c LS

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

1998examfinal-soln - IE 221 OPERATIONS RESEARCH...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online