Question

Review Problem Use for 1 7) A bakery prepares both cakes and cookies. Each batch of cakes requires 4 hours in the oven and 1 hour in the decorating room Each batch of cookies needs 3 hours in the oven and 2 hours in the decorating room. The oven is available no more than 12 hours a day, while the decorating room can be used no more than 6 hours a day. How many batches of cakes and cookies should the bakery make in order to madinize profts if cakes produce a proft of $15 per batch and cookies produce a profit of $25 per batch? Letx-the mmber of batches of cakes and y - the mmber of batches of cookies.) 1.) In order to maximize profits, z, from the two items to be prepared, state the objective fiunction? Total hours Available Cakes (x) Cookies (y) Oven Decorating Room 2) Which is the constraint for the use of the oven? 3) Which is the constraint for the use of the decorating room? 4) Which other constraints are needed? 5) On the graph below, graph feasible region for all of the constraints? o.) Identify the corner points. 7.) Determine the corner point which maximizes the profit. Explain what that means

Answer 1

batches -no ''t batches-ot0 Cookies "d iective hle eaun 15 s no. baten of caka & 25 batch okies Max 15x+ 25 Cakes 4 okies 0 Dec Room 12 2. For the ouen,the Constraint is IS 2. Hx+ 34 412 3 Simi tha dacorating room inoi 4)Tha otha constroins ata non- cantmainstiex&can taka onlu non -nugatve values

90 a rbiect 20 conaidu equalities To dauo -the 0 o__ → (3,0) Al on 2.

ot tha peaai blu're ion c) Tha- corner paina 2CR(o, 3) o)A(3 obtained whure B is imult aneous olving tha2 equatians 2 54-2 ) Cornes paink Prot Z- 15x+ 25 B(s1-2,y2)+25(24) 7 Maxim 2.4): 18. 102 This meansthat we must maka 1.2 batches batchas cookies to maxima.--.