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NaserCo Wants to display it products within 10,000 feet square according to the following Data: Cost of Other Cost of Sales Needed space Product storing extra each each price per of each Unit Unit Unit (in feet) Unit A 50 2 5 80 20 B 90 3 7 115 15 ? 180 5 10 250 30 D 230 7 8 40 per unit 300 NaserCo decided to 1
NaserCo Wants to display it products within 10,000 feet square according to the following Data: Cost of Other Cost of Sales Needed space Product storing extra each each price per of each Unit Unit Unit (in feet) Unit A 50 2 5 80 20 B 90 3 7 115 15 ? 180 5 10 250 30 D 230 7 8 40 per unit 300 NaserCo decided to 1. Display at least 10 units of each Product A and B. 2. Display at most 20 units of product C and D. 3. the capital prepared for buying is 250000 dinar. Find the Linear programming form of the above problem.
Expert Solution
Assume a, b, c and d represent the number of units of A, B, C and D respectively. We want to maximize profit subject to the constraints.
Profit from each product = Sales price - Cost of unit - Cost of storing - Other extra cost
Hence, profit per unit from
A = 80-50-2-5 = 23
B = 115-90-3-7 = 15
C = 250-180-5-10 = 55
D = 300-230-7-8 = 55
Hence objective function is:
Maximize 23a + 15b + 55c + 55d
Subject to
Storage space
20a+15b+30c+40d <=10000
Number of units requirement
a>=10
b>=10
c<=20
d<=20
Capital cost
50a+90b+180c+230d<=250000
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