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The amount of labor available in fabrication is 82 hours/day, whereas in finishing19 hours/day. Because each pair of Jordanelle skis requires 3.5 labor-hours and each pair of Deercrest skis requires 4 labor-hours in the fabricating department, the total labor used in fabrication is 3.5 Jordanelle + 4 Deercrest.

Note that the dimensionsof these terms are (hours/pair of skis)(number of pairs of skis produced per day) = hours. Similarly, for the finishing department, the total labor used is 1 Jordanelle + 1.5 Deercrest. Therefore, the appropriate constraints are:

Fabrication: 3.5 x Jordanelle + 4 x Deercrest <= 82

Finishing: 1 x Jordanelle + 1.5 x Deercrest <= 19

For the market mixture constraint "Number of pairs of Deercrest skis must be at least twice the number of pairs of Jordanelle skis," we have

Deercrest >= 2 x Jordanelle

It is customary to write all the variables on the left-hand side of the constraint. Thus, an alternative expression for this constraint is

Deercrest - 2 x Jordanelle >= 0

The difference between the number of Deercrest skis and twice the number of Jordanelle skis can be thought of as the excess number of Deercrest skis produced over the minimum market mixture requirement. Finally, nonnegativity constraints are written as

Deercrest >= 0

Jordanelle >= 0

The decision variables are the number of pairs of, each type of ski to produce each day. Because SSC makes a net profit of $50 on the Jordanelle model and $65 on the Deercrest model, then, for example, if we produce 10 pairs of Jordanelle skis and 20 pairs of Deercrest skis during one day, we would make a profit of ( $50/pair of Jordanelle skis) ( 10 pairs of Jordanelle skis) + ($65/pair of Jordanelle skis) (20 pairs of Deercrest skis) = $500 + $1,300 = $1,800. Because we don't know how many pairs of skis to produce, we write each term of the objective function by multiplying the unit profit by the decision variables we have defined:

Maximize Total Profit = $50 Jordanelle + $65 Deercrest

What is the optimal solutions for the number of Jordanelle and Deercrest products?

Option 1. Jordanelle 4.75 and Deercrest 9.5

Option 2. Jordanelle4.95 and Deercrest 9.5

Option 3. Jordanelle 4.95 and Deercrest 10

Option 4. Jordanelle 4.75 and Deercrest 10