Two plastic cup factories, Cups R Us and Cupomatic, can produce cups printed with the image of your choice. At Cups R Us, the mandatory setup and design cost is ZAR350 and the cost per cup is ZAR8.50. (a) Develop a linear model for the cost,
C, of an order at Cups R Us based on the number of cups, n. (b) Write down a reasonable domain and range for your model. (c) Use your model to calculate the cost of an order of: (i) 100 cups (ii) 200 cups (iii) 400 cups. (d) Calculate the average cost per cup for: (i) 100 cups (ii) 200 cups (ili) 400 cups. (e) Hence, give a reason why, in general, it is more cost-effective to order more cups. Cupomatic charges ZAR2150 for 200 cups and ZAR3750 for 400 cups. (f) Develop a linear model for the cost, D, of an order at Cupomatic based on the number of cups, n. (g) Write down a reasonable domain and range for your model. (h) Interpret the gradient of your model in context. (i) Use your linear model to predict the cost of 600 cups. ) For orders of more than x cups, it is more cost-effective to order from Cupomatic. Find the value of x.
