Denis wants to start a cake project. He wants to make lots of them and make a profit. His costs are going to be 60000sh for the oven, marketing, and other costs. The total cost of all expenses on each cake made is 500 & p, where p is the number of cakes made.
Task:
Help Denis find the minimum number of cakes he should make and the selling price for each cake such that he does not make a loss.
Answer (1)
To help Denis find the minimum number of cakes he should make and the selling price for each cake to avoid making a loss, let's break down the costs and revenues.
Fixed Costs : These are costs that do not change with the number of cakes he makes. The fixed cost here includes expenses for the oven, marketing, and other costs, totaling 60,000 shillings.
Variable Costs : These are costs that depend on the number of cakes made. It's stated that the total cost of all expenses on each cake is 500 shillings. Therefore, the variable cost for 'p' cakes is 500p shillings, where 'p' is the number of cakes.
Total Costs : The total cost for making 'p' cakes would be the sum of fixed and variable costs: [ \text{Total Cost} = 60000 + 500p \
Revenue : For Denis to not make a loss, his revenue needs to be at least equal to the total cost. To calculate the revenue, we need to consider the selling price of each cake. Let’s denote the selling price per cake by 's' shillings. Therefore, the revenue for selling 'p' cakes is: [ \text{Revenue} = sp \
Breakeven Point : Denis won’t make a loss if his revenue equals his total costs. So the equation for breakeven is: [ sp = 60000 + 500p \ Rearranging the equation gives: [ sp - 500p = 60000 \ [ p(s - 500) = 60000 \ [ p = \frac{60000}{s - 500} \
Conclusion :
For Denis not to incur losses, he needs to sell at least 'p' cakes at a selling price 's' greater than 500 shillings each.
The minimum value of 'p' is reached when 's' is just over 500, which makes 's - 500' a small positive number.
For example, if Denis decides the selling price of each cake is 600 shillings, then: [ p = \frac{60000}{600 - 500} = \frac{60000}{100} = 600 \
Thus, Denis needs to sell at least 600 cakes at 600 shillings each to avoid making a loss. This will ensure that his total revenue covers all his incurred costs.
