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.
Please assist with (x)
if company A manufactures t-shirts and sells them to retailers for US$9.80 each.
It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per
unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.
The demand for its product is p = 15 −
x
125 , its production cost per unit is US$5.00
and its fixed cost are the same as for company A .
(i) Derive the total revenue function, R(x) for company A.
(ii) Derive the total cost function, C(x) for company A.
(iii) Derive the profit function,Π(x) for company A.
(iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company A
in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.
(v) Graph the functions from (d) above on the same axes.
(vi) From your graph, determine the break-even level of output for company A.
(vii) Derive the total revenue function,R(x) for company B.
(viii) Derive the profit function,Π(x) for company B.
(ix) How many t-shirts must company B sell to in order to break-even.
(x) How many t-shirts must company B sell to maximise its profit.
Please assist with (x)
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