The manager of an office supply store can sell 20 boxes of p

The manager of an office supply store can sell 20 boxes of pencils at a price of $3.26 per box. If the price is $1.90, he can sell 36 boxes. The total cost for x boxes of pencils is C( x ) = 0.4.v + 31.25 dollars. Assuming the demand function is linear, find an equation for D( x ). Do not round your answer.

Solution

When price is $3.26 per box, 20 boxes of pencils are demanded.

When price is $1.90 per box, 36 boxes of pencils are demanded.

Let assume that price and demand for pencils is related by a linear demand function of the form -

p = D(x)

However, linear demand function can also be writtent in following slope-intercept form as well.

p = m(q) + b

we have to calculate the value of m and b from the information provided about price and quantity.

The given price and quantity information can be written as ordered pairs (20, 3.26) and (36, 1.90).

m is the slope of equation.

Slope is calculated as follows -

m = (y₂ - y₁)/(x₂ - x₁) = (1.90 - 3.26)/(36 - 20) = -0.08

Now, we will solve for b substituting value of m in equation and using any one of the ordered pairs.

3.26 = -0.08(20) + b

3.26 = -1.6 + b

b = 4.86

So, linear equation is as follows -

p = -0.08(q) + 4.86

Substituting D(x) for p

Linear equation for D(x) is as follows -

D(x) = -0.08(q) + 4.86