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ADVANCED MATH
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ADVANCED MATH
Ballco manufactures large softballs, regular softballs, and hardballs. Each type of ball requires time in three departments: cutting, sewing, and packaging, as shown in Table 65 [in minutes]. Because of marketing considerations, at least 1,000 regular softballs must be produced. Each regular softball can be sold for $3, each large softball, for$5; and each hardball, for $4. A total of 18,000 minutes of cutting time, 18,000 minutes of sewing time, and 9,000 minutes of packaging time are available. Ballco wants to maximize sales revenue. If we define RS = number of regular softballs produced LS = number of large softballs produced HB = number of hardballs produced then the appropriate LP is $$ \begin{aligned} \max z &=3 R S+5 L S+4 H B \\ \text { s.t. } & 15 R S+10 L S+8 H B \leq 18,000 \quad \text{[Cutting constraint]} \\ & 15 R S+15 L S+4 H B \leq 18,000 \quad \text{[Sewing constraint]}\\ 3 R S+4 L S+2 H B & \leq 9,000 \quad \text{[Packaging constraint]}\\ R S & \geq 1,000 \quad \text{[Demand constraint]}\\ R S, L S, H B & \geq 0 \end{aligned} $$ The optimal tableau for this LP is shown in Table 66. a. Find the dual of the Ballco problem and its optimal solution. b. Show that the Ballco problem has an alternative optimal solution. Find it. How many minutes of sewing time are used by the alternative optimal solution? c. By how much would an increase of 1 minute in the amount of available sewing time increase Ballco’s revenue? How can this answer be reconciled with the fact that the sewing constraint is binding? d. Assuming the current basis remains optimal, how would an increase of 100 in the regular softball requirement affect Ballco’s revenue? TABLE 65: $$ \begin{matrix} \text{Bills} & \text{Cutting Time} & \text{Sewing Time} & \text{Packaging Time}\\ \text{Regular softballs} & \text{15} & \text{15} & \text{3}\\ \text{Large softballs} & \text{10} & \text{15} & \text{4}\\ \text{Hardballs} & \text{8} & \text{4} & \text{2}\\ \end{matrix} $$ TABLE 66: $$ \begin{matrix} \text{z} & \text{RS} & \text{LS} & \text{HB} & \text{s1} & \text{s2} & \text{s3} & \text{e4} & \text{a4} & \text{rhs}\\ \text{1} & \text{0} & \text{0} & \text{0} & \text{0.5} & \text{0} & \text{0} & \text{4.5} & \text{M − 4.5} & \text{4,500}\\ \text{0} & \text{0} & \text{0} & \text{1} & \text{0.19} & \text{−0.125} & \text{0} & \text{0.94} & \text{−0.94} & \text{187.5}\\ \text{0} & \text{0} & \text{1} & \text{0} & \text{−0.05} & \text{0.10} & \text{0} & \text{0.75} & \text{−0.75} & \text{150}\\ \text{0} & \text{0} & \text{0} & \text{0} & \text{−0.17} & \text{−0.15} & \text{1} & \text{1.88} & \text{1.88} & \text{5,025}\\ \text{0} & \text{1} & \text{0} & \text{0} & \text{0} & \text{0} & \text{0} & \text{−1} & \text{1} & \text{1,000}\\ \end{matrix} $$
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ADVANCED MATH
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ADVANCED MATH
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Recommended textbook solutionsIf you decide a SWOT analysis is the best tool, the following tips will help you get the most out of it:
Keep your SWOT short and simple, but remember to include important details. For example, if you think your staff are a strength, include specific details, such as individual staff and their specific skills and experience, as well as why they are a strength and how they can help you meet your business goals.
When you finish your SWOT
analysis, prioritise the results by listing them in order of the most significant factors that affect your business to the least.
Get multiple perspectives on your business for your SWOT analysis. Ask for input from your employees, suppliers, customers and partners.
Apply your SWOT analysis to a specific issue, such as a goal you would like to achieve or a problem you need to solve, rather than to your entire business. You can then conduct separate SWOT analyses on individual issues and
combine them.
Look at where your business is now and think about where it might be in the future, as well as where you would like to be.
Consider your competitors and be realistic about how your business compares to them.
Think about the factors that are essential to the success of your business, and the things you can offer customers that your competitors can't. This is your competitive advantage. It's useful to keep these in mind when conducting a SWOT analysis.
Use goals and
objectives from your overall business plan in your SWOT analysis.