The weekly demand and supply functions for sportsman 5 × 7 tents are given by p = −0.1x2 − x + 50 p = 0.1x2 + 2x + 30 respectively, where p is measured in dollars and x is measured in units of a hundred. find the equilibrium quantity.

At equilibrium, the function of demand and supply are equal

The equilibrium quantity where the demand and supply are equal is approximately 1,281 units tents

The reason the above value is correct is as follows:

The given function for the weekly demand for Sportsman 5 × 7 tents is presented as follows;

p = -0.1·x² - x + 50

The given function for the weekly supply for Sportsman 5 × 7 tents is presented as follows;

p = 0.1·x² - 2·x + 30

Where:

p is in dollars, and x is measured in units of a (one) hundred

Required:

To find the equilibrium quantity

Solution:

At equilibrium, the weekly demand and supply are equal, therefore, we have;

-0.1·x² - x + 50 = 0.1·x² - 2·x + 30

(0.1·x² - 2·x + 30) - (-0.1·x² - x + 50) = 0

0.2·x² - x - 20 = 0

Dividing by -0.2 gives;

x² - 5·x - 100 = 0

Which gives;

x ≈ -7.81 or x ≈ 12.81

The positive value of x is used to give;

The equilibrium quantity, x ≈ 12.81 hundred units, which is approximately 1,281 units

The equilibrium quantity is approximately 1,281 units tents

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the demand and supply are in equilibrium when the amount demanded is exactly the same amount as the amount supplied, or namely when demand = supply.

we can't use -20, because the amount cannot be a negative value.

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: