Question

The Uganda Farmers Research Institute suggested to a farmer to spread out at least (4800 , {kg}) of a special phosphate fertilizer and not less than (7200 , {kg}) of a nitrogen fertilizer to raise productivity of crops in his fields. There are two sources for obtaining these mixtures A and B. Both of these are available in bags weighing (100 , {kg}) each and they cost Sh. (40) and Sh (24) respectively. Mixture A contains phosphate and nitrogen equivalent of (20 , {kg}) and (80 , {kg}) respectively, while mixture B contains these ingredients equivalent of (50 , {kg}) each. Determine how many bags of each type the farmer should buy in order to obtain the required fertilizer at minimum cost.​

Answer 1

The farmer should buy 20 bags of mixture A and 88 bags of mixture B to obtain the required fertilizer at minimum cost.

Step-by-step explanation:

To find the minimum cost of obtaining the required fertilizer, we need to determine the number of bags of each type that the farmer should buy. Let's assume the farmer buys x bags of mixture A and y bags of mixture B.

To find the minimum cost of obtaining the required fertilizer, we need to determine the number of bags of each type that the farmer should buy. Let's assume the farmer buys x bags of mixture A and y bags of mixture B.

From the given information, we can set up the following equations:

• 20x + 50y = 4800 (equation for phosphate)
• 80x + 50y = 7200 (equation for nitrogen)

Solving the two equations simultaneously, we can find the values of x and y. Multiplying the first equation by 8 and subtracting it from the second equation, we get:

• -120x + 0y = -2400

Simplifying this equation, we find: -120x = -2400. Dividing by -120 on both sides: x = 20.

Substituting the value of x in the first equation, we find: 20(20) + 50y = 4800. Simplifying: 400 + 50y = 4800. Subtracting 400 from both sides: 50y = 4400. Dividing by 50 on both sides: y = 88.

Therefore, the farmer should buy 20 bags of mixture A and 88 bags of mixture B in order to obtain the required fertilizer at minimum cost.