(1) 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 B. (ii) Derive the profit function,Π(x) for company B. (iii) How many t-shirts must company B sell to in order to break-even.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
(1) 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 B.
(ii) Derive the profit function,Π(x) for company B.
(iii) How many t-shirts must company B sell to in order to break-even.
(iv) How many t-shirts must company B sell to maximise its profit.
(2) 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?
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