Question

You sell Blivets on a sliding-price scale. Price per Blivet p in dollars is given by a linear function of q Blivets. You charge $24 each for an order of 1 Blivet and $18 each for an order of 13 Blivets.

What is the maximum profit? Include units. (Assume that you cannot sell a fraction of a Blivet. The quantity that maximizes profit must be a whole number.)

Answer 1

To find the profit maximizing quantity, calculate total revenue, marginal revenue, total cost, and marginal cost for each output level. Then, analyze the relationships between revenue and cost to determine the quantity that maximizes profit.

Step-by-step explanation:

To calculate total revenue, we multiply the quantity sold by the selling price. For example, at a quantity of 1 unit, the total revenue is $72. At a quantity of 2 units, the total revenue is $144. We can continue this calculation for each output level from 1 to 5 units.

To calculate marginal revenue, we subtract the total revenue at the previous output level from the total revenue at the current output level. For example, the marginal revenue of increasing output from 1 to 2 units is $72. We can continue this calculation for each output level from 1 to 5 units.

To calculate total cost, we sum the fixed cost and the variable cost for each output level. For example, at a quantity of 1 unit, the total cost is $100 + $64 = $164. At a quantity of 2 units, the total cost is $100 + $84 = $184. We can continue this calculation for each output level from 1 to 5 units.

To calculate marginal cost, we subtract the total cost at the previous output level from the total cost at the current output level. For example, the marginal cost of increasing output from 1 to 2 units is $20. We can continue this calculation for each output level from 1 to 5 units.