Furniture Manufacturer Sells Its Product Directly to Consumers and Also $$\text { Comsumers: } Q _ { 1 } = 200 - 5 P _ { 1 }$$

Essay

Furniture manufacturer sells its product directly to consumers and also to retailers. The demand functions of the two types of customers and the total cost function of the furniture company are given below.
$$\text { Comsumers: } Q _ { 1 } = 200 - 5 P _ { 1 }$$ $$\text { Retailers: } Q _ { 2 } = 100 - 10 P _ { 2 }$$ $$T C = 10 + 5 Q$$ What is the optimal level of output and how should the firm distribute its sales?