A company that manufactures pet toys calculates that its costs and revenue can be modeled by the equations C = 15,000 + 1.05x and R = 500x − x2 25 where x is in the number of toys produced in 1 week. Production during one particular week is 5000 toys and is increasing at a rate of 350 toys per week. Find the rate at which the cost, revenue, and profit are changing. (a) cost dC dt = dollars/week (b) revenue dR dt = dollars/week (c) profit dP dt = dollars/week
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.
A company that manufactures pet toys calculates that its costs and revenue can be modeled by the equations
| x2 |
| 25 |
where x is in the number of toys produced in 1 week. Production during one particular week is 5000 toys and is increasing at a rate of 350 toys per week. Find the rate at which the cost, revenue, and profit are changing.
| dC |
| dt |
(b) revenue
| dR |
| dt |
(c) profit
| dP |
| dt |
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