Financial Calculation for University Printery Modules
The image contains a mathematical problem that requires the creation of a formula based on given charging criteria and then using that formula to calculate specific costs. Here is the problem as shown in the image:
"A University printery produces student modules. The printery charges for a module depending on the size of the module, the types of cover and binding used, and the number of books in a print run. The charging formula is as follows: Charge 4 toea per page for paper and collating, and 20 toea per page for cardboard covers. Next add a charge of 5 toea per written page for printing, labour, and other page related costs; and charge K5.00 per printed page for masters that can be used for a minimum of 500 copies. Finally add 20% to the calculated cost to cover for labour costs.
(a) Find a formula for a module that has P paper pages, and C cardboard covers, and is bound. Each module has 2 pages of print and the print run is 500 modules.
(b) Use the formula to find the charges for a module that has 60 pages, 2 covers, and is bound. Each module has 2 pages of print and the print run is 300 modules."
Let's first tackle part (a) to create a formula.
Cost per paper page (for paper and collating): 4 toea
Cost per cardboard cover page: 20 toea
Cost per written page (for printing, labour, and other costs): 5 toea
Cost per printed page for masters: K5.00 (since it can be used for a minimum of 500 copies, there is no need to multiply by the number of modules for this cost)
Let's create the cost formula:
Cost = (P * 4 toea) + (C * 20 toea) + (P * 5 toea) + (2 * K5.00) + 20% of the cost.
To simplify:
Cost = 0.09P + 0.20C + 10 + 0.20(Cost)
We can't have cost on both sides of the equation, so we need to isolate it. Let's factor out the cost on the right side of the equation:
Cost = 0.09P + 0.20C + 10
1.20 * Cost = 0.09P + 0.20C + 10
Cost = (0.09P + 0.20C + 10) / 1.20.
This represents the total cost to produce one module. Now let's use this formula for part (b).
For part (b), we have:
P = 60 pages,
C = 2 covers.
Plugging the numbers into the formula, we get:
Cost = (0.09 * 60 + 0.20 * 2 + 10) / 1.20
Cost = (5.40 + 0.40 + 10) / 1.20
Cost = 15.80 / 1.20
Cost = 13.1667.
So the cost per module with 60 pages, 2 covers, and bound, with 2 pages of print for a print run of 300 modules, is approximately K13.17.
