Mathematics for Social Science Solution

Topics: Microsoft Word, Type, Profit Pages: 3 (408 words) Published: November 17, 2014
SOLUTION GRADED ASSIGNMENT # 2 (5%)
This Assignment tests your knowledge of some aspects of course material covered in various Topics. Prepare your response as a Microsoft Word document and submit in the Drop Box for Assignment 2 before the closing time. All submissions must contained a signed Coursework Accountability Statement declaring the work to be entirely yours. Assignments without the Accountability Statement will not be marked.

The deadline for uploading this Graded Assignment is 3.30 pm (EC time) on Wednesday November 5th, 2014.
Question 1 - Inequalities
A company makes two types of space-savers, english and italian. Each english type requires 3 hours, 2 hours, and 2 hours, while each italian requires 2 hours, 1 hour, and 4 hours for cutting, assembling, finishing respectively.

The company has 300 hours available for cutting, 240 hours for assembling and 120 hours finishing . Each english type earns $85 in profit while the italian type earns $75. a. If you are required to find the combinations of both types of space-savers that will [6 mks]

maximize profits, list the inequalities that would be necessarry. Let x be number of english type space-savers made and sold
Let y be number of italian type space-savers made and sold
3x + 2y ≤ 300
2x + y ≤ 240
2x + 4y ≤ 120
x ≥ 0, y ≥ 0

b. From a graph of the inequalities in part 𝑎. , − 𝐲𝐨𝐮 𝐚𝐫𝐞 𝐧𝐨𝐭 𝐫𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐭𝐨 𝐬𝐮𝐛𝐦𝐢𝐭 𝐭𝐡𝐞 𝐠𝐫𝐚𝐩𝐡 [6 mks]
𝐢𝐧 𝐲𝐨𝐮𝐫 𝐚𝐧𝐬𝐰𝐞𝐫𝐬 − list the vertices of the solution set. The vertices of the solution set will be (0,0); (0,30); (60,0) c.

Which of the combinations of the two types of space-savers will maximize profits?

[2 mks]

P = 85x + 75y
𝐴𝑡 (0,0); P = 85(0) + 75(0) = $0
𝐴𝑡 (0,30);

P = 85(0) + 75(30) = $2250

At (60,0); P = 85(60) + 75(0) = $5100
At (60,0) profits are maximised , produce 60 english type and no italian type. d.

How much will be the maximum profit?

[2 mks]

$5100
Question 2 - Matrices
A security firm borrowed $900,000 for business...
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