Question

A gourmet bakery is planning production of loaves of bread, cakes and pies.

Each loaf of bread requires 450g of flour, 70g of sugar and 4 minutes of labour, and is sold for $3.72.

Each cake requires 650g of flour, 340g of sugar and 17 minutes of labour, and is sold for $16.00.

Each pie requires 350g of flour, 10g of sugar and 16 minutes of labour, and is sold for $12.02.

Each kilogram of flour costs $0.40, each kilogram of sugar costs $6.00, and each hour of labour costs $42.00. Up to 89 kg of flour and 58 kg of sugar can be bought, and 81 hours of labour are available. (Ignore the cost and availability of any other resources.)

Let XB, XC and XP represent the numbers of bread loaves, cakes and pies produced.

Which of the following objective functions represents the bakery's production cost?

Select one:

a. C = 0.32XB + 1.80XC + 0.62XP

b. C = 3.72XB + 16.00XC + 12.02XP

c. C = 3.40XB + 14.20XC + 11.40XP

d. C = 168.60XB + 716.30XC + 672.20XP

e. C = 4.15XB + 13.75XC + 12.68XP

Answer 1

We know that,

Item	Quantity	Cost in $
Flour	1000 gm	0.4
Sugar	1000 gm	6
Labour	60 min	42

Therefore, for each loaf of bread will cost $3.4 calculated as follows:

Item	Quantity	Cost in $
Flour	450 gm	(0.4/1000)*450 = 0.18
Sugar	70 gm	(6/1000)*70 = 0.42
Labour	4 min	(42/60)*4 = 2.8
	Total	3.4

Similarly, each cake will cost $14.2.

Item	Quantity	Cost in $
Flour	650	0.26
Sugar	340	2.04
Labour	17	11.9
	Total	14.2

And each pie will cost $11.4.

Item	Quantity	Cost in $
Flour	350	0.14
Sugar	10	0.06
Labour	16	11.2
	Total	11.4

Therefore, the correct answer is

c. C = 3.40XB + 14.20XC + 11.40XP