Question

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

Answer 1

A.

Total Revenue= (Price of each unit)*( Number of units sold)

So, R(x)= 9.80x where x is the quantity of output sold

B.

Total cost= Total fixed cost+ Total variable cost

Variable cost is the cost dependent upon number of units produced. So for example, the output produced is 0, the variable costs too would be 0

At the same time, fixed costs refer to costs which have to be incurred independent of the quantity of output.

C(x)= 2625+ 2.30x

C.

Profit= total revenue- total cost

= 9.80x - (2625+2.30x)

= 9.80x - 2625 - 2.30x

= 7.50x -2625