The daily demand of type I, type II and type III is respectively 600 loaves, 750 loaves and 500 loaves. The per unit cost to the bakery of the ingredient A,B,C and D is respectively #0.10, #0.07, #0.05 and #0.4 . If the bakery sells the bread for #0.60 for type I, #0.04 for type II and #0.05 for type III, using multiplication only, Determine the following, (1).The ingredients required to fill the daily order(2). the cost for each type of Bread(3). Cost of ingredient required to fill the order.(4). Revenue realized from filling this order and the resultant profit.
so, have you set up your matrices?
If the vectors are
D for demand (3x1)
C for cost
R for revenue,
I for ingredients (3xn)
#1. DTI (1xn)
and so on
Yes, I have set up the matrices. But your solution is not yet clear to me. Pls explain better Sir
The daily demand of type I, type II and type III is respectively 600 loaves, 750 loaves and 500 loaves. The per unit cost to the bakery of the ingredient A,B,C and D is respectively #0.10, #0.07, #0.05 and #0.04 . If the bakery sells the bread for #0.60 for type I, #0.04 for type II and #0.05 for type III, using multiplication only, Determine the following, (1).The ingredients required to fill the daily order(2). the cost for each type of Bread(3). Cost of ingredient required to fill the order.(4). Revenue realized from filling this order and the resultant profit.
The question is not complete what about the quantity of ingredients we need per bread type.This is from AGE-UI right?
Yes sir...From UI. Thought it was complete though. Thanks Peter
To find the answers, we need to perform some calculations using the given information. Let's break it down step by step:
(1) The ingredients required to fill the daily order:
To determine the ingredient quantities needed, we will multiply the daily demand of each bread type by the respective ingredient's unit cost:
Type I:
- Ingredient A: 600 loaves * #0.10 = #60
- Ingredient B: 600 loaves * #0.07 = #42
- Ingredient C: 600 loaves * #0.05 = #30
- Ingredient D: 600 loaves * #0.40 = #240
Type II:
- Ingredient A: 750 loaves * #0.10 = #75
- Ingredient B: 750 loaves * #0.07 = #52.50
- Ingredient C: 750 loaves * #0.05 = #37.50
- Ingredient D: 750 loaves * #0.40 = #300
Type III:
- Ingredient A: 500 loaves * #0.10 = #50
- Ingredient B: 500 loaves * #0.07 = #35
- Ingredient C: 500 loaves * #0.05 = #25
- Ingredient D: 500 loaves * #0.40 = #200
Therefore, the ingredients required to fill the daily order are as follows:
Type I:
- Ingredient A: #60
- Ingredient B: #42
- Ingredient C: #30
- Ingredient D: #240
Type II:
- Ingredient A: #75
- Ingredient B: #52.50
- Ingredient C: #37.50
- Ingredient D: #300
Type III:
- Ingredient A: #50
- Ingredient B: #35
- Ingredient C: #25
- Ingredient D: #200
(2) The cost for each type of bread:
To calculate the cost for each type of bread, we sum up the cost of ingredients required for each type:
Type I:
- Cost = #60 + #42 + #30 + #240 = #372
Type II:
- Cost = #75 + #52.50 + #37.50 + #300 = #465
Type III:
- Cost = #50 + #35 + #25 + #200 = #310
(3) Cost of ingredients required to fill the order:
To determine the total cost of ingredients required to fill the order, we sum up the costs of each type:
Total cost of ingredients = Cost of Type I + Cost of Type II + Cost of Type III
Total cost of ingredients = #372 + #465 + #310 = #1147
(4) Revenue realized from filling this order and the resultant profit:
To find the revenue and profit, we multiply the selling price by the daily demand for each type:
Type I:
- Revenue = 600 loaves * #0.60 = #360
- Profit = Revenue - Cost of Type I = #360 - #372 = (#12) loss
Type II:
- Revenue = 750 loaves * #0.04 = #30
- Profit = Revenue - Cost of Type II = #30 - #465 = (#435) loss
Type III:
- Revenue = 500 loaves * #0.05 = #25
- Profit = Revenue - Cost of Type III = #25 - #310 = (#285) loss
The total revenue realized from filling this order = Revenue from Type I + Revenue from Type II + Revenue from Type III
Total revenue = #360 + #30 + #25 = #415
Total resultant profit = Total revenue - Total cost of ingredients
Total profit = #415 - #1147 = (#732) loss
Therefore, the bakery would have a loss of #732 from filling this order.