# 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.

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...