Witchs brew company manufactures and sells three potions that all use gargoyle e

Question

Witchs brew company manufactures and sells three potions that

all use gargoyle eyelashes as an Witch As an

ingredient. The high demand for all three of these potions exceeds

the supply of gargoyle eyelashes that witches brew is able to buy

from its supplier. Information is as follows:

Beauty potion,: selling price $100, variable cost per bottle 70,

Eyelashes required Per bottle 2, sales demand in units 1, 000.

Luck potion: selling price 120, vc per bottle 84, eyelashes

required 3, sales demand in units 1, 500

Smart potion: selling price 200, vc per bottle 130, eyelashes 5,

Sales demand 1800

A) how many eyelashes would be required to satisfy demand for

all 3 products?

B) each year witches brew is only able to buy 14,000 gargoyle

eyelashes. Using only the information above, basing the decision

solely on maximizing net operating income, how many bottles, if

any, of each potion should witches bre make?

C) a new supplier is found that has eyelashes available to sell.

How many eyelashes would witches brew need to purchase? What is the

maximum amount witches brew would be willing to pay per eyelash?

Assume the normal cost of an eyelash is $10

Explanation / Answer

You have total fixed costs of $65,000, which apparently includes 6,000 eyelashes. If we allocate the entire 65,000 to eyelashes, we have (65,000) / (6000) = 10.83 per eyelash
Variable costs per bottle of $70, $84, and $130

We should consider profitability of each potion.

Profit per bottle of Passion Potion at $112 is
100 - (70 + (2 x 10.83)) = 16.34

Profit for Luck Potion at $88
136 - (88 + (3 x 10.83)) = 15.51

Profit for Smart Potion
224 - (134 + (5 x 10.83)) = 35.85


Since we are limited to 6000 eyelashes, we could make a maximum of
6000/2 = 3000 Passion Potion
but we are further limited by demand to 1400
Maximum possible profit = 1400 x 16.34 = 22,876

6000/3 = 2000 Luck Potion
further limited by demand to 1900
Maximum possible profit = 1900 x 15.51 = 29,469

6000/5 = 1200 Smart Potion
NOT limited by demand (2200)
Maximum possible profit = 1200 x 35.85 = 43,020

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