Problem

Humbug Hammocks produces two types of hammocks for camping: the AsymmetricHammock and the Bridge Hammock. The Asymmetric Hammock has a contributionmargin of $120 and the Bridge Hammock has a contribution margin of $260. The essentialresources required to make the hammocks are sewing hours and a special fabric calledM50 with a finish that stops the fabric from ripping. Each product uses these resources inthe following quantities:

                                     Asymmetric       Bridge
Sewing hours                      7                    15
M50 fabric (metres)              10                  14

Humbug can only get access to 500 square metres of M50 fabric per month. The companyhas two experienced sewing staff who can put in a maximum of 400 hours per month, totalfor the two people. To keep inventories at a minimum, Humbug does not want to produceany more than the monthly demand of 30 units for the Asymmetric Hammock and 20 unitsfor the Bridge Hammock.

Management would like to determine the best product manufacturing mix to maximizecontribution margin. Which linear program describes this objective? Let A represent theAsymmetric Hammock and B the Bridge Hammock.

a) Maximize $120A + $260B

Subject to:

7A + 15B ≤ 500

10A + 14B ≤ 400

A ≤ 30; B ≤ 20

A ≥ 0; B ≥ 0

b) Maximize $120A + $260B

Subject to:

7A + 15B ≤ 400

10A + 14B ≤ 500

A ≥ 30; B ≥ 20
A ≥ 0; B ≥ 0

c) Maximize $120A + $260B

Subject to:

7A + 10B ≤ 400

15A + 14B ≤ 500

A ≤ 30; B ≤ 20

A ≥ 0; B ≥ 0

d) Maximize $120A + $260B

Subject to:

7A + 15B ≤ 400

10A + 14B ≤ 500

A ≤ 30; B ≤ 20

A ≥ 0; B ≥ 0.