Detail

We know that Lane will maximize profits by trying to sell where MR = MC. Unfortunately our table doesn't give us either bit of information directly. It does however give price and quantity as well as total revenue (P x Q). Since we know that she is selling her pizzas at $15 we can determine the MR of the 6^th pizza. If we then determine the MR of the 7^th pizza we will know the range of possible MCs.

A quick way to accomplish all this is to simply compute the MR column for this table as shown below. This isn't necessary, but it may be helpful. Remember though that MR is just the change in revenue due to a change in sales by a single unit, so its just the difference between TR each time sales are increased by a unit. Note that the MR of the 6^th pizza is 10 so we know that MC can't be greater than 10, otherwise it would not have been profitable to sell the 6^th pizza and she would have raised price to $16 and sold 5 pizzas. The MR for the 7^th pizza is 8 so if MC were 8 or below she would have lowered price to $14 and sold 7 pizzas.

Q	P	TR	MR
1	20	20	20
2	19	38	18
3	18	54	16
4	17	68	14
5	16	80	12
6	15	90	10
7	14	98	8
8	13	104	6

16. The data in Table 1 above are for Lane, the only vendor of brick oven baked goat cheese and avocado pizzas at a sporting event. Q is the number of pizzas sold each hour, P is the price in dollars and TR is the total revenue (just P X Q). If the vendor determines that her profit maximizing price per pizza is $15 then her marginal cost for each pizza must be:

over $6 but no more than $8. If this were the case she would have sold 8 pizzas at $13 each.
over $8 but no more than $10.
over $10 but no more than $12. If this were the case she would have sold 5 pizzas at $16 each.
over $12 but no more than $14. If this were the case she would have sold 4 pizzas at $16 each.
over $14 but no more than $15. If this were the case she would have sold 3 pizzas at $18 each, but MC could have been as high as $16 and this would be true too.