An up-and-coming drug company needs to decide production levels for the upcoming
ID: 352447 • Letter: A
Question
An up-and-coming drug company needs to decide production levels for the upcoming week. The company sells three types of drugs, Jomentum, Zapitol, and Pakoderm, each of which is produced in batches. The labor requirements, profit per batch, and weekly demand for each type of drug is given below, along with the company’s weekly capacity (labor hours).
Drug
Profit per batch
Labor hours required/batch
Weekly Demand
Manufacturing
Quality Testing
Jomentum
29
30
13
52
Zapitol
21
25
8
130
Pakoderm
62
32
19
67
Weekly capacity
(labor hours)
4000
3200
The output for an LP solution is provided below.
Adjustable Cells
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$12
Production Jomentum
52
0
29
1E+30
3.80
$C$12
Production Zapitol
12
0
21
3.17
21
$D$12
Production Pakoderm
67
0
62
1E+30
83.12
Constraints
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$G$24
Jomentum Demand
52
4
52
9.87
52
$G$25
Zapitol Demand
12
0
130
1E+30
118.16
$G$26
Pakoderm Demand
67
83
67
9.25
67
$B$25
Manufacturing Needed
4000
1
4000
2954
296
$B$26
Quality Testing Needed
2044
0
3200
1E+30
1156.28
The objective is to come up with the production volumes (number of batches) of the three products to maximize profit. We denote the production volumes of Jometum, Zapitol, and Pakoderm by XJ, XZ, and XP, respectively.
Which one represents the objective function? (Profit per batch is selling price minus the variable cost.)
56XJ + 39XZ + 110XP
29XJ + 21XZ + 62XP
30XJ + 25XZ + 32XP
27XJ + 18XZ + 48XP
What is the maximum profit under the optimal solution?
5914
6021
112
131
Drug
Profit per batch
Labor hours required/batch
Weekly Demand
Manufacturing
Quality Testing
Jomentum
29
30
13
52
Zapitol
21
25
8
130
Pakoderm
62
32
19
67
Weekly capacity
(labor hours)
4000
3200
Explanation / Answer
The objective function is minimum or maximum condition for the problem. The objective coefficient described in second table describes the objective function.
Thus, it is 29XJ + 21XZ + 62XP
Maximum Profit is sum product of coefficient in objective function and final value (Table 2)
Maximum Profit = 29*52 + 21*12 + 62*67 = 5914
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