Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $30,000/day to operate, and it yields 50 ez of gold and 3000 or of her each of a day The Horseshoe Mine costs $16,000/day to operate, and it yields 75 oz of gold and 1000 oz of silver each of y day. Company management has set a target of at least 650 ot of gold and 18,000 af silver (a) How many days should each mine be operated so that the target can be met at a minimum cost? The minimum is C- 288000 at (x,y)-0,18 1) (b) Suppose C-cx+ 16,000y. Find the range of values that the Saddle Mine's daily operating cost, the coefficient cofx, can assume without changing the opti scs (c) Find the range of values that the requirement for gold can assume s (requirement for gold) s (d) Find the shadow price for the requirement for gold. (Round your answer to the nearest cent)

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $30,000/day to operate, and it yields 50 oz of gold and 3000 oz of silver each of a day
The Horseshoe Mine costs $16,000/day to operate, and it yields 75 oz of gold and 1000 oz of silver each of y day. Company management has set a target of at least 650 oz of gold and 18,000 of
silver.
(a) How many days should each mine be operated so that the target can be met at a minimum cost?
The minimum is C - 288000
at (x,y)-(0,18
(b) Suppose C cx + 16,000y. Find the range of values that the Saddle Mine's daily operating cost, the coefficient c of x, can assume without changing the optimal auton
SCS
(c) Find the range of values that the requirement for gold can assume.
s (requirement for gold) s
(d) Find the shadow price for the requirement for gold. (Round your answer to the nearest cent.)
S
Transcribed Image Text:Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $30,000/day to operate, and it yields 50 oz of gold and 3000 oz of silver each of a day The Horseshoe Mine costs $16,000/day to operate, and it yields 75 oz of gold and 1000 oz of silver each of y day. Company management has set a target of at least 650 oz of gold and 18,000 of silver. (a) How many days should each mine be operated so that the target can be met at a minimum cost? The minimum is C - 288000 at (x,y)-(0,18 (b) Suppose C cx + 16,000y. Find the range of values that the Saddle Mine's daily operating cost, the coefficient c of x, can assume without changing the optimal auton SCS (c) Find the range of values that the requirement for gold can assume. s (requirement for gold) s (d) Find the shadow price for the requirement for gold. (Round your answer to the nearest cent.) S
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