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 maximis its profit.

Answer 1

Answers pgno- Now here from given that, @ ③ we get, R(60) = 9.80) x - 2625 - (2.30) X R() = 7.5x – 2625] @ [C(O) = 2625 +(2.30) 2 @ 17 (2) = 9.80 (6) - [2625+2.30 (32] I (Q) 9.80 (0) 2.30 () - 2625 --[TTC) = 7,5% - 2625 x RCA C(x) 50 100 - 2250 -1875 -1500 - 1125 2740 2855 2170 ,150 200 3085 250 - 750 3200 300 -375 3315 350 0 3430 Hoo 375 3545 450 750 3660

Pgnol-2 (0) © ROC) A c) 36607 2740 A so 100 150 200 250 3003 so 100 150 200 250 300 350 400 450 X 350 00 -2250 In the above graph, break even occurs (total revenue = total cost) when out put level is 350. (Vid Total Revenue [TR] = PxQ = 15%-50%125) Vill profit of company B = TR-TC. poofie of company B = 15x -(x/125) -2,625-5X

(pquo; (ie Break even of a company occurs when Total revenue a total cost TR = P xa TR = 15x -(x" /125) T = Fixed cost tvariable Cost 2,625 + 5% : TC- At boeak even point, 1596-(x*(125) = 2,625 +52 .'. r = 375 To maximize profit derivative of profit function must be zero, Derivative of profit function : 10 -0.0168 =0 x = 625 when out put is 625 : Profit of from B is maximum