Modeling Costs for the General Store
1. Remember the form of a quadratic function equation: y = f(x) = ax2 + bx + c
2. You will use: W(x) = -0.1x2 + bx + c where (-0.1x2 + bx) represents the store’s variable costs and c is the store’s fixed costs.
3. Choose a value between 10 and 20 for b; that value does not have to be a whole number.
4. So, W(x)is the store’s total monthly costs based on the number of items sold, x.
5. Think about what the variable and fixed costs might be for your fictitious storefront business – and be creative. Start by choosing a fixed cost, c, between $5,000 and $10,000, according to the following class chart (make sure the combination of your b and your c do not match exactly any of your classmates’):
| If your last name starts with the letter | Choose a fixed cost between |
| A–E | $5,000–$5,700 |
| F–I | $5,800–$6,400 |
| J–L | $6,500–$7,100 |
| M–O | $7,200–$7,800 |
| P–R | $7,800–$8,500 |
| S–T | $8,600–$9,200 |
| U–Z | $9,300–$10,000 |
6. Post your chosen c value in your subject line, so your classmates can easily scan the discussion thread and try to avoid duplicating your cvalue. (Different c values make for more discussion.)
7. Your monthly cost is then, W = -0.1x2 + bx + c.
8. Substitute the c value chosen in the previous step to complete your unique equation predicting your monthly costs.
9. Next, choose two values of x (number of items sold) between 50 and 100. Again, try to choose different values from classmates.
10. Plug these values into your model for W and evaluate the monthly business costs given that sales volume.
11. Discuss results of these cost calculations and how these calculations could influence business decisions.
12. Is there a maximum cost for your General Store? If so, how many units must be sold to produce the maximum cost, and what is that maximum cost? How would knowing the number of items sold that produces the maximum cost help you to run your General Store more efficiently?
