Q1(i) If the demand curve for a particular commodity is p = −0.09x + 51 and thetotal cost function C(x) = 1.32x2 + 11.7x + 101.4,where x is the level of production. Find(a) The revenue R(x) and profit Π(x).(b) All values of x for which production of the commodity is profitable.(ii) The total cost of manufacturing x units during the daily production run at a factory, isC(x) = x2 + x + 900 dollars. Usually, x(t) = 25t units are manufactured during thefirst t hours of production.(a) Express the total manufacturing cost as a function of t.(b) How much will have been spent on production by the end of the third hour?(c) When will the total manufacturing cost reach $11,000?
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.
Q1
(i) If the demand curve for a particular commodity is p = −0.09x + 51 and the
total cost function C(x) = 1.32x
2 + 11.7x + 101.4,where x is the level of production. Find
(a) The revenue R(x) and profit Π(x).
(b) All values of x for which production of the commodity is profitable.
(ii) The total cost of manufacturing x units during the daily production run at a factory, is
C(x) = x
2 + x + 900 dollars. Usually, x(t) = 25t units are manufactured during the
first t hours of production.
(a) Express the total manufacturing cost as a function of t.
(b) How much will have been spent on production by the end of the third hour?
(c) When will the total manufacturing cost reach $11,000?
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