Sara's Sensible Critters makes two kinds of catnip toys: balls (x₁) and mice (x₂) . The relationship between demand and price for balls and mice is:
x₁ = 1800 - 150p₁
x₂ = 1500 - 300p₂
The cost for a catnip ball is $2 and for the mouse, $3.
Sara has only 200 ounces of catnip on hand. A ball uses a tenth of an ounce and a toy mouse uses one-quarter of an ounce.
-Write the appropriate expression for profit.

Question

Quizplus · Accepted Answer

The expression for profit is:
Profit = (Revenue from balls) + (Revenue from mice) - (Cost of catnip used for balls) - (Cost of catnip used for mice)

Profit = p1x1 + p2x2 - ($0.2)x1 - ($0.75)x2

To maximize profit, we need to differentiate the profit function with respect to p1 and p2 and set the derivatives equal to zero.

dProfit/dp1 = x1 - 0.2 = 0
dProfit/dp2 = x2 - 0.75 = 0

Solving these equations, we get:
x1 = 0.2
x2 = 0.75

Substituting these values in the demand functions, we get:
p1 = $10
p2 = $8.33

Substituting these values in the profit function, we get:

Profit = (10x1 + 8.33x2) - (0.2x1) - (0.75x2)
Profit = 2x1 + 3x2

Therefore, the appropriate expression for profit is:
Max Z = (p1 - 2)x1 + (p2 - 3)x2

Option C is the correct answer.

Sara's Sensible Critters Makes Two Kinds of Catnip Toys: Balls