(a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. (i) What is the average rate of change of the profit for this product when between 150 and 250 units are sold? (ii) Write the equation of the profit function for this product. (iii) How many units give break-even for this product?
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) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895.
(i) What is the average rate of change of the profit for this product when between 150 and 250 units are sold?
(ii) Write the equation of the profit function for this product.
(iii) How many units give break-even for this product?
(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 − 4q 2 where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass
(i) Write an equation giving profit as a function of the number of lightweight compasses produced.
(ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?
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