The United Auto Workers went on strike support the employees of the Detroit News, Detroit Free Press, and USA Today. This is an
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The first step you need to do to solve this problem is to calculate the contribution margin per unit for each model:
Model a12 b22 c124
Sales Price per unit 50 100 400
Less: Variable Cost per unit 35 70 300
Contribution Margin per unit 15 30 100
The next step is to calculate the weighted-average contribution margin per unit for the sales mix using the following formula:
Model a12 CM per Unit ×
Model a12 Sales Mix Percentage<span>
+ Model b22 CM per Unit × Model b22 Sales Mix Percentage
+ Model c124 CM per Unit × Model c124 Sales Mix Percentage
<span>= Weighted Average Unit Contribution Margin (WACM)</span></span>
Contribution Margin per unit 15 30 100
X Sales Mix Percentage 60% 15% 25%
WACM 9 4.5 25
Weighted Average Unit Contribution Margin (sum) 38.5
The next step is to find the break-even point using the WACM.
<span> <span><span> <span> Total Fixed Cost </span> <span> $269,500 </span> </span> <span> <span> ÷ Weighted Average CM per Unit </span> <span> $38.50 </span> </span> <span> <span> Break-even Point in Units of Sales Mix </span> <span> 7,000 </span> </span> </span></span>
The next step is to calculate the number of units of each model at break-even point
<span> <span><span> <span> Model </span> <span> a12 </span> <span> b22 </span> <span> c124 </span> </span> <span> <span> Sales Mix Ratio </span> <span> 60% </span> <span> 15% </span> <span> 25% </span> </span> <span> <span> × Total Break-even Units </span> <span> 7,000 </span> <span> 7,000 </span> <span> 7,000 </span> </span> <span> <span> Product Units at Break-even Point </span> <span> 4,200 </span> <span> 1,050 </span> <span> 1,750 </span> </span> </span></span><span> </span>
Answer:
Profit-maximizing price per drug treatment is $2,000
Explanation:
The "cost of production" (cost of providing all treatments) is given by the area under the cost curve
(The cost curve is the straight line C = 10Q)
It is a right triangle with one side being the quantity (Q) and the other being the cost of the last unit being produced (10Q)
So the cost of production is:
Revenue is given by P * Q = (3,000 - 10Q) * Q
Profit = Revenue - Cost of production = 3,000Q - -
To find maximum, take derivative and solve for:
3,000 - 30Q = 0 => Q = 100
Profit-maximizing quantity is 100. The price will then be P = 3,000 - 10*100 = $2,000