chegg Witches brew company manufactures and sells three potions that all use gar
ID: 2577555 • Letter: C
Question
chegg Witches 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
each year witch's brew is only able to budy 6000 garagoyle eyelashes .annual fixed cost at wich's brew are 45000
required
a) how many bottles of eachpotion should wich's brew make this year to maximixe profit?
b)based on these restrictions, what is the maximum annual operatin income that witch's brew can make each year?
c) what is the maximum price witch's bre would pay for 30 more gargolye eyelashes if they wre available?
Explanation / Answer
a. Calculation of number of bottles of each type to be produced and sold
1. Calculation of Contribution per unit eyelash
Particulars
Beauty Potion
Luck potion
Smart Potion
Sales
100
120
200
VC
70
84
130
Contribution per unit
30
36
70
Eyelashes required
2
3
5
Contribution per eyelash
15
12
14
Number of Units that can be produced from 6000 eyelashes
6,000 / 2 = 3,000
6,000 / 3 = 2,000
6,000 / 5 = 1,200
Demand
1,000
1,500
1,800
Since Contribution per eyelash is higher in case of Beauty potion, company should first produce all the units of Beauty potion and the remaining eyelashes should be used for producing Smart potion having next best contribution margin and then Luck Potion
Unit to be produced
Type of Bottle
Units required per bottle
Demand that can be met
Eyelashes remaining
Total Contribution
Beauty Potion
2
1,000
6,000 – 2,000 = 4,000
2 x 1,000 x $15 = 30,000
Smart Potion
5
4,000 / 5 = 800 units
4,000 – 4,000 = 0
5 x 800 x $14 = 56,000
Luck Potion
3
0
0
0
Total Contribution
86,000
2. Annual Operating Income = Total Contribution - Fixed Costs
= 86,000 - 45,000 = $41,000
Particulars
Beauty Potion
Luck potion
Smart Potion
Sales
100
120
200
VC
70
84
130
Contribution per unit
30
36
70
Eyelashes required
2
3
5
Contribution per eyelash
15
12
14
Number of Units that can be produced from 6000 eyelashes
6,000 / 2 = 3,000
6,000 / 3 = 2,000
6,000 / 5 = 1,200
Demand
1,000
1,500
1,800
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