The profit P, in thousand of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows. P = −0.2N2 + 3.6N − 9 (a) Express using functional notation the profit at a production level of 4 items per year. P( ) Calculate that value. thousand dollars (b) Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero. N = (smaller value) N = (larger value) (c) Determine the maximum profit if the manufacturer can produce at most 18 in a year. thousand dollars
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
The profit P, in thousand of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows.
P( )
Calculate that value.
thousand dollars
(b) Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero.
| N = | (smaller value) |
| N = | (larger value) |
(c) Determine the maximum profit if the manufacturer can produce at most 18 in a year.
thousand dollars
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