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satela [25.4K]
2 years ago
13

Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contri

bution per tire are given in the following table. Manufacturing Time Hours) Time Available Operation aterial Preparation Tire Building Curing Final Inspection rofit Tire Economy tiresPremium tires Hours 600 650 580 120 4/3 1/2 1/2 1/5 $12 2/4 1/3 $10 Answer the following assuming that the company is interested in maximizing the total profit contribution.
a. What is the linear programming model for this probiem?
b. How many tires of each model should Gatson manufacture?
c. What is the total profit contribution Gatson can earn with the optimal production quantities?

Business
1 answer:
EastWind [94]2 years ago
8 0

Answer:

(a)Let X1 be the number of economy tires and X2 be the number of premium tires.

Objective function:

Maximize Z, where Z = 12X1 + 10X2

Subject to constraints

4X1/3 + X2/2 <= 600

4X1/5 + X2 <= 650

X1/2 + 2X/4 <= 580

X1/5 + X2/3 <= 120

X1, X2 = Z

(b) Check attachment for spreadsheet

(c) The maximum profit that can be obtained is $6032

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Read 2 more answers
Crystal Apple Sales Company began 2014 with cash of $2,000, inventory of $3,600 (200 crystal apples that cost $18 each), $2,500
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Answer and Explanation:

a. The computation of ending inventory and cost of goods sold using the three different cost flow assumptions: FIFO, LIFO, and Weighted Average is shown below:-

Cost of goods sold = (200 × $18) + (800 × $20) + (1,040 × (2,040-200-800)

= (200 × $18) + (800 × $20) + (1,040 × $24)

= $3,600 + $16,000 + $24,960

= $44,560

Ending Inventory Under FIFO = (1,200 - 1,040) × (2,040-200-800)

= 160 × $24

= $3,840

Under LIFO method

Cost of goods sold is

= (1,200 × $24) + (800 × $20) + (40 × $18)

= $28,800 + $16,000 + $720

= $45,520

Ending Inventory Under LIFO is

= (200 - 40) × $18

= 160 × $18

= $2,880

Weighted Average cost flow Assumption

Weighted Average cost per apple = Cost of Beginning inventory and purchase ÷ Total apple available

Cost of Beginning inventory and purchases is

= (200 × $18) + (800 × $20) + (1,200 × $24)

= $3,600 + $16,000 + $28,800

= $48,400

Total apples available is

= 200 + 800 + 1,200

= 2,200  

Weighted Average cost per apple is

= $48,400 ÷ 2,200

= $22

Cost of goods sold is  

= 2,040 × $22

= $44,880

Ending Inventory is

= 160 × $22

= $3,520

b. The Preparation of income statement, a balance sheet, and a statement of cash flows under each of the three cost flow assumptions is prepared below:-

Income Statement                       Amount

Sales (2,040 × $40)                     $81,600

Less: Cost of goods sold            ($44,560)

Gross Profit                                  $37,040

Less: Operating Expenses         ($26,000)

Income before income taxes      $11,040

Less: Income tax (30% × $11,280) ($3,312)

Net Income                                     $7,728

Balance Sheet

Assets  

Cash                                                   $9,488

Inventory                                             $3,840

Total Assets                                        $13,328

Liabilities and Stockholder's Equity

Common Stock                                   $2,500

Retained Earnings                              $10,828

Total Liabilities and Equity                $13,328

Working note

cash = (opening + Sales - Purchases - Operating expenses - Income tax expenses )

= $2,000 + $81,600 - $44,800 - $26,000 - $3,312

= $9,488

Retained earning = (Opening + Net Income)

= $3,100 + $7,728

= $10,828

Statement of Cash Flow

Cash Flow from Operating Activities  

Cash Sales                                               $81,600

Payment to Accounts Payable              ($44,800)

Operating Expenses                              ($26,000)

Income tax paid                                      ($3,312)

Net Increase in cash and

cash equivalents                                     $7,488

Add: Opening Cash and

cash equivalents                                     $2,000

Closing Cash and cash equivalents      $9,488

LIFO cost flow Assumption

Income Statement

Sales (2,040 × $40)                                 $81,600

Less: Cost of goods sold                         ($45,520)

Gross Profit                                              $36,080

Less: Operating Expenses                     ($26,000)

Income before income taxes                  $10,080

Less: Income tax (30% × $10,080)             ($3,024)

Net Income                                               $7,056

Balance Sheet

Assets  

Cash                                                           $9,776

Inventory                                                    $2,880

Total Assets                                               $12,656

Liabilities and Stockholder's Equity

Common Stock                                           $2,500

Retained Earnings                                       $10,156

Total Liabilities and Equity                         $12,656

Working note:-

Cash = (opening + Sales - Purchases payment - Operating expenses -Income tax expenses)

= $2,000 + $81,600 - $44,800 - $26,000 - $3,024

= $9,776

Retained earning = (Opening + Net Income)

= $3,100 + $7,056

= $10,156

Statement of Cash Flows  

Cash Flow from Operating Activities  

Cash Sales                                             $81,600

Payment to Accounts Payable            ($44,800)

Operating Expenses                            ($26,000)

Income tax paid                                     ($3,024)

Net Increase in cash and

cash equivalents                                     $7,776

Add: Opening Cash and

cash equivalents                                     $2,000

Closing Cash and cash equivalents       $9,776

Weighted Average cost flow Assumption

Income Statement  

Sales (2,040 × $40)                                   $81,600

Less: Cost of goods sold                         ($44,880)

Gross Profit                                               $36,720

Less: Operating Expenses                       ($26,000)

Income before income taxes                   $10,720

Less: Income tax (30% × $10,720)           ($3,216)

Net Income                                                $7,504

Balance Sheet  

Assets  

Cash                                                           $9,584

Inventory                                                   $3,520

Total Assets                                              $13,104

Liabilities and Stockholder's Equity

Common Stock                                         $2,500

Retained Earnings                                     $10,604

Total Liabilities and Equity                       $13,104

Working note

Cash = opening + Sales - Purchases payment - Operating expenses - Income tax expenses )

= $2,000 + $81,600 - $44,800 - $26,000 - $3,126

= $9,584

Retained earning = (Opening + Net Income)

= $3,100 + $7,504

= $10,604

Statement of Cash Flows

Cash Flow from Operating Activities

Cash Sales                                       $81,600

Payment to Accounts Payable      ($44,800)

Operating Expenses                       ($26,000)

Income tax paid                               ($3,216)

Net Increase in cash and

cash equivalents                              $7,584

Add: Opening Cash and

cash equivalents                            $2,000

Closing Cash and

cash equivalents                               $9,584

8 0
2 years ago
. Which of the following describes a short position in an option? A. A position in an option lasting less than one month B. A po
True [87]

Answer:

D. A position where an option has been sold.

Explanation:

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