Question

Tawfiq Trading Company plans to supply 50,000 cartons of oil in January 2021 with the carton selling for $ 20.

It is predicted that the imported oil will fall by 20,000 if the price of a carton of oil falls by 20%.
develop the Supply Equation formula? ​

Answer 1

`\displaystyle s=5,000p-50,000`

Explanation:

Linear Model

The supply of cartons of oil in January 2021 is predicted to reach 50,000 cartons for Tawfiq Trading Company with the carton selling for $20.

If we call s the supply of cartons and p the price, the ordered pair (p,s) for this condition is (20 ; 50,000).

It's predicted that the supply will fall by 20,000 if the price falls by 20%. The new supply will be 50,000-20,000=30,000 and the new price will be 0.8*$20=$16. This gives us the second point (16 ; 30,000)

The equation of a line passing through points (p1,s1) and (p2,s2) can be found as follows:

`\displaystyle s-s_1=(s_2-s_1)/(p_2-p_1)(p-p_1)`

Substituting the given points:

`\displaystyle s-50,000=(30,000-50,000)/(16-20)(p-20)`

Calculating:

`\displaystyle s-50,000=(-20,000)/(-4)(p-20)`

`\displaystyle s-50,000=5000(p-20)`

Operating and simplifying:

`\displaystyle s-50,000=5,000p-100,000`

`\mathbf{\displaystyle s=5,000p-50,000}`