Let the demand function for a product be given by the function D(q)=1.6q+210, wh

Question

Let the demand function for a product be given by the function D(q)=1.6q+210, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $2,000 and variable costs are $5 per item produced. If 78 items are produced and sold, find the following:

A) The total revenue from selling 78 items (to the nearest penny).


B) The total costs to produce 78 items (to the nearest penny).


C) The total profits to produce 78 items (to the nearest penny. Profits may or may not be negative.).

Explanation / Answer

A)revenue R(q)=(1.6q+210)*q

R(78)=((1.6*78)+210)*78

R(78)=6645.6

B)Cost C(q)= 2000+ 5q

C(78)= 2000+ (5*78) ==>C(78)= 2000+ 390 ==>C(78)= 2390

C)profit =revenue -cost= 6645.6-2390 =4255.6

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