Question

Maximum Revenue When a wholesaler sold a product at $30 per unit, sales were 296 units per week. After a price increase of $5, however, the average number of units sold dropped to 276 per week. Assuming that the demand function is linear, what price per unit will yield a maximum total revenue

Answer 1

The price to yield a maximum revenue = $52 per unit

Explanation:

Given Data:

Selling price = $30 per unit

Unit per week = 296 units

Price increase = $5

Unit dropped = 276 units

For demand function;

D = ax +b ------------------------1

when x = $30 and D = 296, equation 1 becomes

30a + b = 296 ----------------2

When price increases by $5, x = 30+5 = $35 and D = 276

Equation 1 becomes,

35a + b = 276 -------------------3

Solving equation 2 and 3 simultaneously to obtain a and b, we have

Making b subject in equation 2-

b = 296 - 30a ---------------4

putting equation 4 into equation 3, we have

35a + 296 - 30a = 276

5a = -20

a = -4

Putting the value for a into equation 4, we have

b = 296 -30(-4)

= 296 +120

= 416

Equation 1 becomes;

D = -4x + 416

revenue function is given as;

R(x) = D*x

= (-4x + 416)x

= -4x² + 416x

For maximum revenue, dR(x)/dx = 0

dR(x)/dx = -4x² + 416x = 0

-8x + 416 = 0

x = 0 - 416/-8

x = -416/-8

x = $52

Therefore, the price to yield a maximum revenue = $52 per unit