Stroika Concrete makes bags of easyuse concrete for the DIY

Stroika Concrete makes bags of easy-use concrete for the DIY market. The company mixes their concrete using two ingredients, \"Great Grit\" and \"A1 Aggregate\". Great Grit costs L1 per kilogram and consists of 20% fine sand, 40% coarse sand and 40% gravel. A1 Aggregate costs L0.75 per kilogram and consists of 10% fine sand, 50% coarse sand and 40% gravel. Each bag of Stroika concrete must contain at least 2kg of fine sand, 2 kg of coarse sand and 6 kg of gravel. What is the least cost combination of ingredients that will satisfy the minimum requirements, and what will be the cost of these ingredients per bag of concrete produced?

Solution

Great Grit

= 20 % fine + 40% coarse + 40% gravel

= (0.20 * 2) + (0.40 * 2) + (0.40 * 6)

= 3.6 Kg.

Total cost of Great grit = 3.6 * 1 = $ 3.60

A 1 Aggregate:-

= 10 % fine + 50% coarse + 40% gravel

= (0.10 * 2) + (0.50 * 2) + (0.40 * 6)

= 3.6 Kg.

Total cost of A1 Aggregate = 3.6 * 0.75 = $ 2.70

Conclusion:- Total cost of Great grit = $ 3.60 and Total cost of A1 Aggregate = $ 2.70 and Overal cost per bag of concrete produced = 3.60 + 2.70 = $ 6.30