Ensure my profit margin, discounts provided, markup asked.

Question

My mathematical problem :

I would like to know the Mark Up percentage that I need to add based on the below data.

Given :

• Turnover = 100€

• Profit Margin (desired) = 20%

• Discount 1 = 30%
  100% of my turnover get 30% discount

• Discount 2 = 5%
  30% of my turnover get 5% discount (Group A)

• Discount 3 = 6%
  50% of my turnover get 6% discount (Group B)

• Discount 4 = 5%
  20% of my turnover get 5% discount (Group C)

Discount Policy : A 30% discount set to all of my clients, 6% discount if someone belongs to Group A, 5% discount if someone belongs to Group B and 6% discount if someone belongs to Group C. Note that someone could belong to more than one groups.

Desiderata :

Mark up (%) = ?

Answer 1

Your words in policy disagree with the bullets, assuming policy wording is correct.

You have to explain if the discounts are additive or multiplicative, i.e. a person from group A gets $30\%$ and $6\%$ so is it $36\%$ total discount or he pays $0.7 \cdot 0.95 = 0.665$, a $33.5\%$ discount. Once you get it, do the following:

• For each group, compute the fraction $f_a,f_b,f_c$ they would pay for your product
• If turnover percent per group is $t_a, t_b, t_c$, the total return from group $A$ is $f_a \cdot t_a$. What is the total return from the entire policy?
• Since you want $20\%$ profit from $100$, how much gross sales do you want to actually make after all sales are finished?
• Finally, markup percentage $m$ is used to make the total generated sales equal the desired sales gross amount. Can you write down a linear equation for $m$ and solve it?