Answer to Question #123981 in Operations Research for Richarda Kuksakon

Question

Linear program assignments A farmer owns 5 hectares of land and thinks of the type of crop to be planted with rice or corn. currently, the rainy season so that by planting rice can provide income of 20 tons / hectare and if planting corn can produce as much as 15 tons / hectare. so that the results obtained are as expected, the farmer employs farm laborers with the assumption that if planting rice requires 30 hours-person / week and corn 10 hours-person / week. The available working time every week does not exceed 40 hours. at the same time the government issued a policy so that farmers produce at least 10 tons of corn for each harvest. The current price of rice is sold at Rp. 5000 / kg and the price of corn is sold at Rp. 4000 / kg. how is the formulation of this problem so that the farmer can optimize his land use?

Answer 1

Workings

Let x represent the number of kg of rice

Let y represent the number of kg of corns

Constraints: x ≥ 0, y ≥ 0

30x + 10y ≤ 40 Simplify by dividing coefficients of x and y by their L.C.M.

Therefore;

30x/30 + 10y/30 ≤ 40/30

x + 0.3y ≤ 1.3 ………………………………. (i)

y ≥ 10 ………………………………………. (ii)

Number of kg to be produced per ha

Rice         = (20 x 1000) kg

                = 20,000kg

Corns       = (15 x 1000) kg

                = 15,000kg

Land optimization

Rice: Selling price per kg = Rp5000

                    20,000kg     = (20,000 x 5,000) Rp

                                         = 100,000,000 Rp

Corns: Selling price per kg = Rp 4,000

15,000 kg                         = (4,000 x 15,000) Rp

                                         = Rp 60,000,000

Maximum outcome will be;

5,000x + 4,000y = k

Therefore; Planting Rice will earn maximum income of Rp 100,000,000.