The Ministry of Highways requires a mixture of sand and salt to spread on BC%u20

ID: 2985498 • Letter: T

Question

The Ministry of Highways requires a mixture of sand and salt to spread on BC%u2019s roads during the

winter. The mixture must contain not more than 70% sand and not less than 10% salt. (It may

also contain gravel, dirt, and other materials.) Products available include Carol%u2019s Road Mix, with

75% sand and 2% salt for $50/ton, and Gord%u2019s Grits, with 60% sand and 6% salt for $120/ton.

Pure salt costs $800/ton. What combination of the two mixtures and salt meets the requirements

with the lowest cost per ton?

Let x = tonne of pure salt in 1 tonne of mixture

y = tonne of carol.

z = tonne of Gord grit

So, objective function S = 50y + 120z + 800x the price of the mixture

Constraints -

x+y+z =1 // This mixture must be 1 tonne

.75y+.6z <= .7 // total % of sand is less than 70%

0.02*y+0.06z + x >= 0.1 //Salt must be 10%

The optimal solution is x = 0.08 y = 091 z = 0 and hence price 111.22

I used phpsimplex to calculate it http://www.phpsimplex.com

Comment if you have any doubt