A bakery and coffee shop operate next to each other downtown. The bakery sells bags of donuts (d) for $30 each and the coffee shop sells bags of coffee {1:} for 515. Making donuts and ooffee is costless, but each shop needs to advertise to attract customers. Some of the customers lured by the advertising from one shop will also make a purchase at the other shop. Specically, the bakery needs to spend slid) = g % on advertising in order to sell at bags of donuts and the coffee shop must spend C(k) = i E on advertising in order to sell I: bags of coffee. c. The city looks out for its business owners and hires a consultant to determine how much the two shops should advertise in order to maximize total prots. What level of d and I: does the consultant recommend? \"It'd + II]: = 301! - C(d) + 15]: C(k) Maximize this function get the first derivative and set it equal to zero For :1: so add) at\") = u _. 30 = (21) + (1) ad ad 15 3o 30 an 2d 21' 30 2" k 450 2d. 14: = i- = ) = 15 30 15 15 F k 15 add) 615(k) o 15 2k 1! d 15 2:: 2d. 15 : = 'o = b = 1 or 6].: at: 15 30 30 15 30 2" d 225 2k :1 - _ _) _ _ 2dk=4k2d 5 4d=5k4d=zk 450 2 5]: It 450 5k 2k 450 3k k\" 300 = i : b = ) = (4 ) 2 2 2 5 d" = z(300) = 375