If 219 items are produced and sold, find the following:

Question

Let the demand function for a product be given by the function , where  is the quantity of items in demand and  is the price per item, in dollars, that can be charged when  units are sold. Suppose fixed costs of production for this item are  and variable costs are  per item produced. If  items are produced and sold, find the following:

A) The total revenue from selling 219 items (to the nearest penny). 

B) The total costs to produce 219items (to the nearest penny). 

C) The total profits to produce 219 items (to the nearest penny. Profits may or may not be negative.). 

Answer 1

Hello, Sara,

I'm not certain I understand the problem, but here's what I did. Use the equation to calculate the price of the item by entering the 219 units sold. [This seems backward to me, but I'll assume the price was set to create a demand of 219 units]. I get a price of $19.10/item. The cost to produce 219 item is the $5,000 fixed cost plus the variable cost of $9/item. This sums to a cost of $6,971 total for 219 items. Sales is 219 times the sales price of $19.10, to yield total sales of $4,182.90. Subtract the cost of sales from this number to produce a profit of -$2,788.10. [Time to change the business model]..

I hope this helps,

Bob