Question

Goldilocks needs to find at least 12 lbs gold and 18 lbs silver to pay monthly rent. Each day in Mine 1 she finds 2 lbs gold and 2 lbs silver. Each day in Mine 2, she finds 1 lb gold and 3 lbs silver. Set up and solve using either LPsolve or on-line solver How many total days in the mines

Answer 1

Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days

Explanation:

Requirement : 12 Ibs gold and 18 Ibs silver to pay monthly rent

Mine 1 ; 2 Ibs of gold , 2Ibs of silver.

Mine 2; 1 Ib of gold , 3 Ibs of silver

using LP

Gold : aX1 + bX2 ≥ 12 ---------- ( 1 )

Silver: cX1 + dX2 ≥ 18 --------- ( 2 )

where; X1 = days spent in Mine 1

X2 = days spent in Mine 2

Total days spent in mines : X1 + X2 =

a = Gold found in mine 1 = 2

b = Gold found in mine 2 = 1

c = silver found in mine 1 = 2

d = silver found in mine 2 = 3

Back to equations 1 and 2

2X1 + X2 ≥ 12 ----------- ( 3 )

2X1 + 3X2 ≥ 18 ------------ ( 4 )

solving equations 3 and 4

= 0 + 2X2 ≥ 6 ∴ X2 ≥ 3 days ( days spent in mine 2 )

Input value into ( 3)

2X1 ≥ 12 - 3 = 9

∴ X1 ≥ 4.5 days ( days spent in mine 1 )

Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days