Can sum1 help me to formulate this problem???
1)Formulate the following. A family has 2 farms A and B which have 200 and 500 acres of land respectively. It has £20,000 available for investment, to be allocated between the 2 farms. 4000 person hours of labour is available on farm A and 6000 person hours on farm B. If necessary, extra labour can be bought in on farm A at a cost of £8 per person hour.
Cash income is obtained from 2 crops, wheat and oats, and 2 forms of livestock, hens and cows.
The resource requirements (which are assumed to be identical for the 2 farms) and the net profit for the above are as follows:
(I can't do a table. I hope this bit is clear!)
That first line is the headings. the products are oats, wheat, cows and hens. The 'land' column is 2, 4, 10, 0. the 'investment' column is 0, 0, 500, 20. The 'labour (person hours)' column is 40,40,30,2 and the 'net profit per unit' column is 20,30,100,5.
PRODUCT, LAND(acres), Investment(₤s), Labour(person hours), Net profit per unit
Oats(per ton) 2 0 40 20
Wheat(per ton) 4 0 40 30
Cows (per animal) 10 500 30 100
Hens(per bird) 0 20 2 5
In addition owing to limitations in the number of buildings for animals, the maximum number of cows and hens each firm can accommodate is 10 and 200 respectively on farm A and 20 and 200 respectively on farm B.
The family has already signed a contact to supply at least 20 tons of wheat to a company. The family wishes to maximise profits.