A farmer uses two types of fertilizers. A 50-lb bag of fertilizer C contains 8 l

Question

A farmer uses two types of fertilizers. A 50-lb bag of fertilizer C contains 8 lb of nitrogen., 2 lb of phosphorus and 4 lb potassium. A 50-lb bag of fertilizer D contains 5 lb each of nitrogen, 260 lb of phosphorus and 360 lb of potassium. The minimum requirements for a filed are 440 lb of nitrogen, 260 lb of phosphorus and 360 lb of potassium. If fertilizer C costs $30 and fertilizer D costs $20 for a 50 lb bag, find the amount of each type of fertilizer the farmer should use the minimize hos cost while still meeting the minimum requirements. What is the minimum cost? When costs are minimized, are there any excess ingredients used?

Graph the feasible region and show all work.

Explanation / Answer

These are the linear programming

It seems 260 and 360 for fertilizer B are given wrongly.

Hence solutions may not be right.

Nitrogen 8 5 Phosphorous 2 260 Pottassium 4 360 8x+5y > 440 2x+260y>260 Cost 30x+20y 4x+360y>360

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