Linear programming questions

[Hye]

A produce grower decides to buy fertiliser containing three nutrients A, B and C to spread on her paddocks. The minimum needs are 160 units of A, 200 units of B and 80 units of C. There are two popular brands of fertiliser on the market: Fast Grow, costing $4 a bag, contains three units of A, five units of B and one unit of C. Easy Grow, costing $3 a bag contains two units of each nutrient.
If the grower wishes to minimise her costs while still maintaining the nutrients required, how many bags of each brand should she buy?


Thanks

[pooshwaltzer]

Need = 160A + 200B + 80C

Fast Grow = 4 = 3A + 5B + 1C

Ezy Grow = 3 = 2A + 2B + 2C

Address nutrient C first as it is closest hurdle...
40 EG will get you 80C, 80B, 80A ... IE. $1.50 per C as opposed to FG's $4 per C

80A and 120B left...Address B next...
28 FG and 1 EG will give 78A and 2A respectively so 80A altogether ... again, application of marginal cost factor

The above also means 142 - 120 = 22B in surfeit so B is also covered...
Min Cost = (28*4) + (41*3) = 112 + 123 = $235