Megley Cheese Company is a small manufacturer of several different cheese produc
ID: 2692103 • Letter: M
Question
Megley Cheese Company is a small manufacturer of several different cheese products. One of the products is a cheese spread that is sold to retail outlets. Jason Megley must decide how many cases of cheese spread to manufacture each month. The probability that the demand will be six cases is 0.1, for 7 cases is 0.30, 8 cases is 0.5, and for cases is 0.1. The cost of every case is $45, and the price Jason gets for each case is $95. Unfortunately, any cases not sold by the end of the month are of no value, due to spoilage. How many cases of cheese should Jason manufacture each month?Explanation / Answer
Cost
45
Revenue
95
PRODUCED
COST
PRODUCED
COST
PRODUCED
COST
PRODUCED
COST
6
270
7
315
8
360
9
405
Demand
profit
Expected profit
profit
Expected profit
profit
Expected profit
profit
Expected profit
6
0.1
300
30
255
25.5
210
21
165
16.5
7
0.3
300
90
350
105
305
91.5
260
78
8
0.5
300
150
350
175
400
200
355
177.5
9
0.1
300
30
350
35
400
40
450
45
TOTAL
300
340.5
352.5
317
Producing 8 cases provides the highest total expected profit ($352.50)
the operations manager of a musical instrument distributor feels that demand for bass drums may be related to the number of tv apperances by the popular rock group Green Shades. During the preceeding month. The manager has collected the data to show on the following table
Demands for Bass Drums Green Shades TV appearnaces
3 3
6 4
7 7
5 6
10 8
8 5
a) graph these data to see whether a linear equation migh describe the relationship between the groups television show and bass drum sales.
b) using the equations presented in this chapter comput the SST, SSE and SSR. Find the least squares regression line for this data.
SSR =
(4-3)^2 + (5-6)^2 + (8-7)^2 + (7-5)^2 + (9-10)^2 + (6-8)^2 =
1 + 1 + 1 + 4 + 1 + 4 =
12
SSE =
(4-6.25)^2 + (5-6.25)^2 + (8-6.25)^2 + (7-6.25)^2 + (9-6.25)^2 + (6-6.25)^2 =
6.25 + 2.25 + 2.25 + 0.25 + 6.25 + 0.25 =
17.5
SST = SSR + SSE
SST = 12 + 17.5 = 29.5
Regression line: y = x + 1
C what is your estimate for bass drum sales if the green shades perfomed on tv 6 times last month?
y = x + 1
y = 6 + 1
y = 7
Cost
45
Revenue
95
PRODUCED
COST
PRODUCED
COST
PRODUCED
COST
PRODUCED
COST
6
270
7
315
8
360
9
405
Demand
profit
Expected profit
profit
Expected profit
profit
Expected profit
profit
Expected profit
6
0.1
300
30
255
25.5
210
21
165
16.5
7
0.3
300
90
350
105
305
91.5
260
78
8
0.5
300
150
350
175
400
200
355
177.5
9
0.1
300
30
350
35
400
40
450
45
TOTAL
300
340.5
352.5
317